When thinBackup runs it only performs the backup on one job (under the jobs folder). It seems like it is continually running throughout the day...when I have the backup scheduled at 2:00AM.
From the log, it runs all day and every minute or so it shows this in the log:
2011-01-24 09:22:14,093 INFO [org.jvnet.hudson.plugins.thinbackup.ThinBackupPeriodicWork] (ThinBackup Worker Thread thread) Started ThinBackup Worker Thread
2011-01-24 09:22:14,094 INFO [org.jvnet.hudson.plugins.thinbackup.ThinBackupPeriodicWork] (ThinBackup Worker Thread thread) Finished ThinBackup Worker Thread. 1 ms

There is also this exception in the log, but I am having a hard time figuring out if it is related:

2011-01-24 09:22:44,120 ERROR [org.apache.catalina.core.ContainerBase.[jboss.web].[localhost].[/hudson].[Stapler]] (http-10.7.0.113-8080-3) Servlet.service() for servlet Stapler threw exception
java.lang.IllegalStateException: getWriter() has already been called for this response
at org.apache.catalina.connector.Response.getOutputStream(Response.java:588)
at org.apache.catalina.connector.ResponseFacade.getOutputStream(ResponseFacade.java:183)
at javax.servlet.ServletResponseWrapper.getOutputStream(ServletResponseWrapper.java:102)
at javax.servlet.ServletResponseWrapper.getOutputStream(ServletResponseWrapper.java:102)
at org.kohsuke.stapler.ResponseImpl.getOutputStream(ResponseImpl.java:82)
at org.kohsuke.stapler.Stapler.serveStaticResource(Stapler.java:405)
at org.kohsuke.stapler.Stapler.serveStaticResource(Stapler.java:242)
at org.kohsuke.stapler.Stapler.service(Stapler.java:150)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:717)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:290)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:206)
at hudson.util.PluginServletFilter$1.doFilter(PluginServletFilter.java:94)
at hudson.plugins.greenballs.GreenBallFilter.doFilter(GreenBallFilter.java:51)
at hudson.util.PluginServletFilter$1.doFilter(PluginServletFilter.java:97)
at hudson.util.PluginServletFilter.doFilter(PluginServletFilter.java:86)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:235)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:206)
at hudson.security.csrf.CrumbFilter.doFilter(CrumbFilter.java:47)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:235)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:206)
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 org.acegisecurity.ui.ExceptionTranslationFilter.doFilter(ExceptionTranslationFilter.java:166)
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 org.acegisecurity.ui.basicauth.BasicProcessingFilter.doFilter(BasicProcessingFilter.java:173)
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:66)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at hudson.security.ChainedServletFilter.doFilter(ChainedServletFilter.java:76)
at hudson.security.HudsonFilter.doFilter(HudsonFilter.java:164)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:235)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:206)
at org.jboss.web.tomcat.filters.ReplyHeaderFilter.doFilter(ReplyHeaderFilter.java:96)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:235)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:206)
at org.apache.catalina.core.StandardWrapperValve.invoke(StandardWrapperValve.java:235)
at org.apache.catalina.core.StandardContextValve.invoke(StandardContextValve.java:191)
at org.jboss.web.tomcat.security.SecurityAssociationValve.invoke(SecurityAssociationValve.java:190)
at org.apache.catalina.authenticator.AuthenticatorBase.invoke(AuthenticatorBase.java:433)
at org.jboss.web.tomcat.security.JaccContextValve.invoke(JaccContextValve.java:92)
at org.jboss.web.tomcat.security.SecurityContextEstablishmentValve.process(SecurityContextEstablishmentValve.java:126)
at org.jboss.web.tomcat.security.SecurityContextEstablishmentValve.invoke(SecurityContextEstablishmentValve.java:70)
at org.apache.catalina.core.StandardHostValve.invoke(StandardHostValve.java:127)
at org.apache.catalina.valves.ErrorReportValve.invoke(ErrorReportValve.java:102)
at org.jboss.web.tomcat.service.jca.CachedConnectionValve.invoke(CachedConnectionValve.java:158)
at org.apache.catalina.core.StandardEngineValve.invoke(StandardEngineValve.java:109)
at org.apache.catalina.connector.CoyoteAdapter.service(CoyoteAdapter.java:330)
at org.apache.coyote.http11.Http11Processor.process(Http11Processor.java:829)
at org.apache.coyote.http11.Http11Protocol$Http11ConnectionHandler.process(Http11Protocol.java:598)
at org.apache.tomcat.util.net.JIoEndpoint$Worker.run(JIoEndpoint.java:447)
at java.lang.Thread.run(Thread.java:636)