I have been very frustrated in a couple very similar games lately online. In both opponent put me in check in a place that I had only one move. But, I was not in danger as he had no way to checkmate me. In one we both had about the same number of pieces(many pieces left) and in the other I had a large advantage over the other player.
In both cases my opponent just kept putting me in check forcing my king to move back and forth. The online game automatically called the games a draw. I thought the draw rule was when both opponents were even and neither was going to be able to win the game. But, in both of these cases my opponent could have made many other moves. There was no reason to keep making the same move other than to get a draw. But, there was a lot more chess to be played in each case. I guess I just felt like I didn’t want to play with someone that played like that. The intent of the rule is not to use it like this as far as my understanding of it.
I know what you mean. Chess can be frustrating at times. But the three-move-repetition rule is valid all the time, independent of the position, if you have advantage or not does not matter at all. It is perfectly okay for your opponent to use it.
So make sure that your king is safe before you make a move and that your opponent cannot give “eternal checks”.
Before you make your Move, check first MENTALLY what will happen afterwards.
You can avoid these frustrations easily! Just check every move in your head, that your opponent can do after your intended next move, BEFORE you actually execute your move on the board.
Make your move MENTALLY in your head first and analyze the position. If everything is okay then execute your move. This is the only way to avoid gross errors or at least this way you can cut down the probability that you overlooked something like a fork, a check, a forced draw, the loss of material or even checkmate.
Chess is a hard game and requires mental discipline. Don’t make a move in future unless you have checked your move in your head first. This will avoid unnecessary draws and other chess disasters.
Try this from now on, you will see that this method will become second nature after some time. And it will improve your playing strength for sure.
I hope this helps.