Jelly TagScripts maintain a per-thread cache of Tag objects. These Tag objects in turn hold on to their JellyContexts. This tag cache doesn't get GC-ed until the thread is dead, so if there are a large number of HTTP request handling threads, over time the tag cache gets pretty full, results in OutOfMemoryError.
This problem is fixed in Jelly and integrated into stapler 1.197, which gets released in 1.485 through 288827f67166c3159f18babf87b16693f537bb9b.
I'm recording this here to make this backported to LTS.