Hey there
In this specific case, the use of the Adobe CC version is requirable.
I'm working remotely with an agency and Montserrat is the main font used by a specific brand, and this is a job worked simultaneously by different people, so having the same font across the board is necessary to avoid issues.
No one else down the pipeline has been having this issue, just me...
Anyway, I already realized this is not a consistent issue. Some days it happens, some days it doesn't.
Are there any connection issues with your Internet setup? Does your computer have a VPN running? It's possible for fonts synced via Adobe Fonts to disappear in either scenario. I'd also look at other applications or utilities running in the background.
A couple of other common troubleshooting measures you can try: Deleting the font data cache and making the computer re-build it. Logging out of the CC account, rebooting the computer and logging back into the CC account again.
Visually speaking, there is nothing different between the version of Montserrat carried at Adobe Fonts and the version at Google Fonts. It's possible the build version of the font files could be different. However, I wouldn't have both installed at the same time. Just one or the other. If everyone in your team is using Montserrat from Adobe Fonts it's probably best to stick with that if possible.