I have a hard time playing more than one 5 minute blitz game at a time, that is my reason.
If your opponent is letting the time run on his move, then you're not really actively playing that game anyway. How much of your concentration does it drain to not look at a game that your opponent has abandoned ? Zero ?
I guess for me I would prefer to lose rather than sit idle whilst the opponent has quietly slipped away like a coward. In fact I have been known to resign the game when it's obvious the opponent is a clock sucker. My time is worth more than a win.
Then I have an easy solution for you: start another game. You are a premium member, so you can play multiple games at the same time.
If someone is just letting the clock run, just start the next game and play it. In my experience, over 90% of those letting the clock run won't make a move before their time runs out, so just play your new game and enjoy chess and don't bother about the 10% or so you might lose because they make a move at the last second.
This is what I do most of the time, however I RESIGN rather than abandon.
There is no reason to resign, you can have both games active at the same time.
I have a hard time playing more than one 5 minute blitz game at a time, that is my reason.