Tech support needed

I previously posted the following under a different title but got no reply so trying again as I still am experiencing the same problem and looking for a solution.

”On three occasions in last few weeks, I have been  playing games where I thought my opponent had abandoned. I had made a move and their clock continued to count down. This eventually stopped at but with no indication of my having won on time. On later reviewing the game history, I had “lost”.  When this happened today I was able to have conversation with my opponent. We were both sitting watching a screen waiting for the other to play. I could see his clock counting down whilst he could see my clock counting down. Neither of us could make a move on the board.  I eventually lost on time when his clock stalled at and I apparently still had over 6 minutes. What is happening?”

This has just happened to me again. My opponent appears to have offered a draw which I didn’t notice at the time since messages are below the bottom of my visible screen (using a tablet). I have attempted to play a move, which I assume should automatically decline the draw offer, but this has led to the system failing as described above. Again I appear to have timed out although watching my opponents clock running down.  This is frustrating for me, but my opponents probably think that I have just walked off, abandoning the game rather than resigning. They have probably been cursing me for leaving them sitting many minutes waiting for their win.  

Has anybody else experienced this. Why is this happening and how can the problem be resolved?

Addendum

Numbers seem to be removed from my post! When above says “at”, it should be followed by a time, namely

zero colon zero zero point one.