Are you using 'wait to trigger remote builds until no other builds are running'?
If not does it fix your issue? I found I needed both working together for it to be reliable.

If so is the problem that the build gets triggered but is waiting in the queue (as it's waiting for and executor)?

I will see if I can have a look tomorrow. Had a lot on the last week.

It looks like the root issue is that we are not getting a response from the REST API. This is because until the build get's an executor it won't have a REST API page. whenw e try and call the page we get a null or response. There is an update coming for the JSON issue you're seeing, thanks to @scotthains, which will likely fix your issue.

I think this should work because getBuildStatus method takes a null response (from sendHTTPCall) to mean the build has not yet started - the problem with this though is that this means if someone cancels the job before it gets an executor the Remote trigger plugsdsdin will wait indefinitely.

The best way I can see to solve this is to try and get Jenkins Core to give jobs an API page before they get an executor. I'm not sure how easy that would be as, if I remember correctly, the job is a different class of object after it gets and executor and before.

Did you check with the link Maurice posted?

'wait to trigger remote builds until no other builds are running' doesn't fix the issue for me.

Do you have any idea when this JSON update is getting released?

Code changed in jenkins
User: Maurice Williams
Path:
CHANGELOG.md
src/main/java/org/jenkinsci/plugins/ParameterizedRemoteTrigger/RemoteBuildConfiguration.java
http://jenkins-ci.org/commit/parameterized-remote-trigger-plugin/0f704da096418c11c543c36382efc997b6125a2a
Log:
fixing JENKINS-22427 (https://issues.jenkins-ci.org/browse/JENKINS-22427)

this fix is part of the 2.1.2 release done on April 26th