My suggestion is to get a call trace (with strace or similar) of MonitorLM up through when it is clearly hung.
This may be too big to send by email to support@wolfram.com. It can be uploaded
via http://upload.wolfram.com/. For the "Recipient:" field, put
"support@wolfram.com". In the "Additional notes:", mention this discussion, 426035.
Other ideas:
Try starting monitorlm with the option -format text
Try running under a different window manager, if possible.
If available, the contents of /proc/version .
If the computer has a Sysinfo application or similar for showing the configuration and software versions, please send the output from it.