I bought the high tops - Yeah, these will fall apart on you. The only way they won't, is if you don't wear them. However, this is what I did a few days ago and it seems to be working well -- Where the welt was coming apart, I stuck in a little contact cement. The soles on mine were coming off too. I used the contact cement on the soles also - so far, all is good.
NOW - this is something that you should not have to do, but for me, it's been a few days, it's working, so I'm happy. Before you stick contact cement on everything and expect it to work, a word of advice - learn how contact cement works (basically, cover both pieces that will be stuck together, let the cement dry, then stick the two pieces together - you'll get a nice strong bond).