From what your describing, it sounds like the modem may be failing.
But, I would try a factory reset.
Hold the rest button 15-20 sec until power LED flashes rapidly then goes solid.
If that doesn't work, you can also try going back to the previous firmware version by downloading and installing it from a PC.
Having a hard time linking directly, so. Go to the link in my screenshot if one below doesn't work.
https://www.scantool.net/downloads/updates/obdlink_mxp/ I also suggest you put in a support ticket.
https://support.obdlink.com/support/tickets/new Describe or link them to this thread Let them know when you purchased it (3 year warranty)
Kind regards,
Shawn