If in the process of development new versions are added to a project, the version pickers
for the jira fields "Affect Versions" and "Fix Versions" are immediately updated.

The version pickers for any custom filed of type version are not!

Jira needs to be stopped and restarted in order to get the custom field version pickers up-to-date.
I tried out all operations possible from the web interface like reindexing and flushing the cache,
but it did not help.
This is a problem because to restart jira you need login access to the server.
In our company, only the separate IT dept. has, so not even I as a web-based jira administrator
can do the update.
Since adding a new release is a very common operation which happens quite often,
asking another department to restart jira is not really a solution!