A big merge or a change involving lots of files easily produces a huge comment, especially when "Record Scm changes" is turned on.
Jira typically has a limit on the comment size, and when Jenkins attempts to put in such a huge comment, the updater fails as below:
These JIRA update failures are not reflected in the job console log (it only puts out several [Jira] Updating issue KEY-1234 ), so there's no way to tell what went wrong unless you look up the actual Jenkins log.
1. report JIRA update failures in the job console log
2. add a parameter ("max. comment length" or whatever) in the global configuration for the Jira plugin. Truncate generated comments according to this limit (possibly, attempting to close any fancy formatting tags at the end, but that's not critical).
It's also quite possible that one may need to see the SCM details fetched by "record SCM changes" in Jenkins' web UI, but omit them in the JIRA comments. I do not see how to achieve this having only a single checkbox in the Configuration.