It will lose tension like all strings. I can't perceive tension loss directly (unless I check with a Stringmeter), but I can see the effects in my game.
A lot of it depends on whether you are used to the feeling of new strings or old strings. People who don't play that much and never restring are used to dead strings; a fresh string job might feel weird and too tight. Conversely, if you're used to new strings, old strings will feel soft and mushy.
Let's say you like fresh strings. Your technique is calibrated for that particular feeling. As the string loses tension, your game will adapt and compensate automatically. You may find yourself starting to miss more, especially those tough shots you 'used to make.' It's easier to compensate for lost tension during easy rallying, but when you're pushed hard, your muscle memory will revert to the shot it 'remembers,' except this time with a lower tension than your game was calibrated for. Sure, you'll get it after a couple of tries, but how many shots will you miss before you've recalibrated your running forehand (never mind starting over again after you restring)? Stretch this out for the duration of just one hitting session and you have a recipe for lots of swearing and general unhappiness with your game.
The effects are more pronounced the harder you hit the ball. Even at the intermediate level, players may not even notice or care, and simply take responsibility for getting the ball in, period. As you improve and start blasting more and more of your shots, you're talking a much lower margin of error.
At high levels, you're hitting hard and still need max consistency, that means the best contact you can muster as you're running and scrambling around the court. You can't control the incoming ball, so that means consistent stroke technique...which will be difficult to develop if your stroke is constantly compensating for things like tension loss. Of course, good players will adapt and improve regardless...but all players will benefit from minimizing variables that can complicate this already complex game. This is why people restring so often (they like fresh strings) or wait a few days after restringing before playing, or stepping on their strings (they like broken-in strings).
Of course, this is assuming you already know how to move your feet and get in position for every shot.
