As you can see here, the loudspeaker connects to the motherboard via pressure contacts, which is probably why pushing on them helps the connection. I can think of two fixes:

1. Your phone is less than a year old, so it should still be covered by a manufacturer's warranty. Contact them and have them "fix it" (they'll probably send you a new phone).

2. Remove the rear case and clean the speaker contacts with a high concentration alcohol. Also inspect them for any damage. The problem that lies here, though, is that if you find out that there's any damage Motorola won't honor the warranty, since you opened it. Option 1 seems like the way to go.

They are known to go out on the Droid Razr and the Razr Maxx. You can find a replacement Droid Razr Loud Speaker