According to the rules:
Being prone may also give a character total cover instead of normal cover (for example, being prone behind a low wall), subject to the GM's discretion.
So yes, this can work. But not in every situation, with every kind of cover. For example, dropping prone around a corner shouldn't provide any more cover than standing erect around it.
Dropping prone behind a
car landspeeder should remove cover. Remember: in Star Wars, cars float ;) Admittedly not that high, but if you're 20 feet away, you should be able to see under them with no problem.
Your group's use of readying actions are a perfectly valid way of dealing with this. But you should also remember that you can ready any standard or move action (though oddly, not a swift action, so you can't drop prone). So you can employ many of your powers even when enemies are using this tactic.
Using AoE effects can also work. The rules on auto-fire AOE attacks are a bit odd on cover. Auto-fire weapons won't work if the cover can withstand the fire, but a thrown grenade, as in real life, can flush people out of cover quite effectively.
But most important of all, you need to remember to use your advantages: mobility. By sacrificing their move action just to stand up, they are limiting themselves to being able to shoot or move, but not both. If you advance forward, even if you don't get around their cover that turn, they have to make a choice. They can either get up and run (burn their standard action to move) or shoot you. But they can't shoot and move in the same turn.
Oh, and FYI: if you want to try this trick yourself, being trained in Acrobatics allows you to stand up as a swift action, thus allowing you to retain the option of moving and shooting.