This actually sounds like the browser is doing something strange

yes i just noticed these,if i'm trying from chrome or Firefox its logging off from Jenkins .
But when i'm using Internet Explorer it saving job configuration.
So what is the workaround for these to solve and make it to work even for chrome and firefox

Even with IE I'm facing same issue.

Could also be a compatibility issue with the old version of jenkins you are using I guess but I just tried it with that version and it works for me.
Without more info about exceptions etc from the logs I can't say

I checked log its getting following error for similar job which has Email extension plugin configured

Jan 25, 2017 10:50:02 AM WARNING org.eclipse.jetty.util.log.JavaUtilLog warn
Error while serving https://sdndevops08.sv.avaya.com/jenkins/view/Test_Bed/job/Mail/configSubmit
java.lang.reflect.InvocationTargetException
at sun.reflect.GeneratedMethodAccessor924.invoke(Unknown Source)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.lang.reflect.Method.invoke(Method.java:606)
at org.kohsuke.stapler.Function$InstanceFunction.invoke(Function.java:320)
at org.kohsuke.stapler.Function.bindAndInvoke(Function.java:163)
at org.kohsuke.stapler.Function.bindAndInvokeAndServeResponse(Function.java:96)
at org.kohsuke.stapler.MetaClass$1.doDispatch(MetaClass.java:124)
at org.kohsuke.stapler.NameBasedDispatcher.dispatch(NameBasedDispatcher.java:58)
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:746)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:876)
at org.kohsuke.stapler.MetaClass$5.doDispatch(MetaClass.java:233)
at org.kohsuke.stapler.NameBasedDispatcher.dispatch(NameBasedDispatcher.java:58)
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:746)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:876)
at org.kohsuke.stapler.MetaClass$5.doDispatch(MetaClass.java:233)
at org.kohsuke.stapler.NameBasedDispatcher.dispatch(NameBasedDispatcher.java:58)
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:746)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:876)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:649)
at org.kohsuke.stapler.Stapler.service(Stapler.java:238)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:848)
at org.eclipse.jetty.servlet.ServletHolder.handle(ServletHolder.java:686)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1494)
at hudson.util.PluginServletFilter$1.doFilter(PluginServletFilter.java:135)
at hudson.util.PluginServletFilter.doFilter(PluginServletFilter.java:126)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at hudson.security.csrf.CrumbFilter.doFilter(CrumbFilter.java:49)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:84)
at hudson.security.UnwrapSecurityExceptionFilter.doFilter(UnwrapSecurityExceptionFilter.java:51)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at jenkins.security.ExceptionTranslationFilter.doFilter(ExceptionTranslationFilter.java:117)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.providers.anonymous.AnonymousProcessingFilter.doFilter(AnonymousProcessingFilter.java:125)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.ui.rememberme.RememberMeProcessingFilter.doFilter(RememberMeProcessingFilter.java:142)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.ui.AbstractProcessingFilter.doFilter(AbstractProcessingFilter.java:271)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at jenkins.security.BasicHeaderProcessor.doFilter(BasicHeaderProcessor.java:93)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.context.HttpSessionContextIntegrationFilter.doFilter(HttpSessionContextIntegrationFilter.java:249)
at hudson.security.HttpSessionContextIntegrationFilter2.doFilter(HttpSessionContextIntegrationFilter2.java:67)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at hudson.security.ChainedServletFilter.doFilter(ChainedServletFilter.java:76)
at hudson.security.HudsonFilter.doFilter(HudsonFilter.java:171)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at org.kohsuke.stapler.compression.CompressionFilter.doFilter(CompressionFilter.java:49)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at hudson.util.CharacterEncodingFilter.doFilter(CharacterEncodingFilter.java:81)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at org.kohsuke.stapler.DiagnosticThreadNameFilter.doFilter(DiagnosticThreadNameFilter.java:30)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1474)
at org.eclipse.jetty.servlet.ServletHandler.doHandle(ServletHandler.java:499)
at org.eclipse.jetty.server.handler.ScopedHandler.handle(ScopedHandler.java:137)
at org.eclipse.jetty.security.SecurityHandler.handle(SecurityHandler.java:533)
at org.eclipse.jetty.server.session.SessionHandler.doHandle(SessionHandler.java:231)
at org.eclipse.jetty.server.handler.ContextHandler.doHandle(ContextHandler.java:1086)
at org.eclipse.jetty.servlet.ServletHandler.doScope(ServletHandler.java:428)
at org.eclipse.jetty.server.session.SessionHandler.doScope(SessionHandler.java:193)
at org.eclipse.jetty.server.handler.ContextHandler.doScope(ContextHandler.java:1020)
at org.eclipse.jetty.server.handler.ScopedHandler.handle(ScopedHandler.java:135)
at org.eclipse.jetty.server.handler.HandlerWrapper.handle(HandlerWrapper.java:116)
at org.eclipse.jetty.server.Server.handle(Server.java:370)
at org.eclipse.jetty.server.AbstractHttpConnection.handleRequest(AbstractHttpConnection.java:489)
at org.eclipse.jetty.server.BlockingHttpConnection.handleRequest(BlockingHttpConnection.java:53)
at org.eclipse.jetty.ajp.Ajp13Connection.access$2900(Ajp13Connection.java:45)
at org.eclipse.jetty.ajp.Ajp13Connection$RequestHandler.headerComplete(Ajp13Connection.java:237)
at org.eclipse.jetty.ajp.Ajp13Parser.parseNext(Ajp13Parser.java:492)
at org.eclipse.jetty.ajp.Ajp13Parser.parseAvailable(Ajp13Parser.java:158)
at org.eclipse.jetty.server.BlockingHttpConnection.handle(BlockingHttpConnection.java:72)
at org.eclipse.jetty.server.bio.SocketConnector$ConnectorEndPoint.run(SocketConnector.java:264)
at winstone.BoundedExecutorService$1.run(BoundedExecutorService.java:77)
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1145)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:615)
at java.lang.Thread.run(Thread.java:745)
Caused by: javax.servlet.ServletException: This page expects a form submission but had only {}
at org.kohsuke.stapler.RequestImpl.getSubmittedForm(RequestImpl.java:998)
at hudson.model.Job.doConfigSubmit(Job.java:1205)
at hudson.model.AbstractProject.doConfigSubmit(AbstractProject.java:795)
... 76 more

You don't have a reverse proxy or something in between? that suggests either the browser is not sending the data or its being filtered/currupted by something

So what is the solution to resolve issue.
Why only if E-mail Extension plugin is configured for job its unable to save job config.
For remaining jobs without these plugin everything is working fine.

Only thing I can suggest is upgrade jenkins

Thanks David Issue was resolved after upgrading Jenkins to latest version