Actually, it's not a Harmony, but an import Harmony copy. If you notice, the Harmony has a squared off headstock, unlike the OP's uke. My mom has an identical ukulele to the OP's uke. However, the name, like yours, is missing, only showing that bit of glue. The other identifying marker is the wood saddle, instead of the plastic saddle Harmony uses.
However, to me, it's a pretty decent sounding uke, very solidly built, and I don't see any issues with the thing not lasting forever. This is the ukulele my mom brings to lead singing at a Kids Club I help lead.
Dan