I've had this before on some of my personal builds. You either popped a solder weld in your speaker or the speaker itself is coming apart. When you press on it, you're reconnecting the wire. I'm assuming these aren't under warranty anymore. If any of them are, contact customer support about getting it/them fixed.
Otherwise, pull your battery/speaker/board thing out. Take your batteries out first. Then, look at the speaker holder, on the side where the board is. There are two little holes. You can take a paper clip or something else very thin (blade retention wrench will probably work) and press it into that hole. The speaker will pop out, as they're just press fit in there. Once you have the speaker out, you'll be able to assess the damage. It's a relatively easy fix, you'll just need a cheap soldering iron or gun and some solder. Walmart, Target, whatever other discount store you have in your area, should sell what you need for a few dollars. (if you were working with a soundboard, you'd want a better one) I know the Walmart I work at has a little kit with a cheap iron and some solder for around $10. Now, it's your choice, but you can either solder the existing speaker back in or put in a new one. You can get that style of 28mm speaker really cheap on Amazon. I usually buy them in 4 packs for a few dollars. (Ultrasabers doesn't sell the speakers without the whole holder) Anyway, once you do your repair, test it (of course) and then press the speaker back into the holder until it snaps in place. That's all there is to it.