I tried running this question through gog's absolutely idiotic virtue support and got nowheres. So I will try here if this game is actually even supported by the developers on gog.
I updated Kingdoms of Amalur: Re-Reckoning yesterday with the full game install of version 1.7 lol or 101. Today I see there is a patch to take the game from 1.7 to 1.7a. That patch won't install on my version of the game. So guess what the full game version you had up yesterday won't patch itself today with the latest patch.

Same thing for me. I'll have to redownload the entire thing but I'll give it at least several more days to see if there are going to be new patches. This one seems to run well enough, it does have a few bugs though. There are no patch notes anywhere so I have no idea what the difference between 1.7 lol and 1.7a are. At first I thought maybe GOG got hacked or something, but it was up a few hours later so I just went and grabbed it. Still playing through the expansion, it does have a good amount of length, albeit the quality isn't super duper great.

gog galaxy might be able to help you with only downloading the parts that need updating. I think it has that feature.

If it does, then it's probably better to use that for these games that update frequently.

I understand wanted the patches to work though. I've never had one work..