Some things in life are dumb.
This is one of them.
The original premise doesn't make sense.
Lost perpetual check (draw by repetition, or, offered draw). Your opponent stops moving after trying to continue play. You have mate in one. (So, make that move and end the game, or schedule a pre-move.)
Don't look away and then claim your opponent stopped moving and something is wrong with the rules because you lost a game.
That's your problem you looked away. Not your opponent's problem. It's not a problem with the rules. You lost. Your opponent won. Cry cry, tear tear, whine whine, complain complain.
If you don't like the rules, then don't play, or go setup your own website where you can whimsically change the rules to meet your needs and field everyone's complaints such that results are rolled back to appease whims possibly against your own. (Or, your whims might change tomorrow when one of your own rules bites you in the arse.)
A win is a win, even if it is on time. Your opponent's time-management is his or hers alone, with time given on the clock for the game. (There are a couple of these whiner / complainer threads going about poor time management. We set time limits and various time constraints on games for a reason.) Just as it your own poor time management to look away or step away (go to lunch).
So let's just change the rules and require a specified time-limit for when someone must make a move ... because today we've got an "oh, poor me" situation.
You come here and complain, and, everybody shrugs. I'm shrugging right now as I'm laughing. And tomorrow, and the day after, I'll be shrugging because it doesn't matter. It's petty. For an
@oldegeezer -- you sure have some growing-up to do.