Couple of options come to mind if you're fairly confident in batch file syntax.
First, if the Access DB is indeed still open, you could check that the lock file (.LDB) exists. Once Access closes, the lock file will be deleted. You could to a rudimentary loop in your batch file waiting for that file to delete.
Alternatively, though I'm not sure if Monarch does this (I don't use it in batch files), is if Monarch returns an errorlevel on failure. You could check that errorlevel and again if it fails just loop your routine until it's successful.
Thank you Nick Osdale-Popa. Having communicated with others on this I think it may make more sense to have Monarch export them as .txt files and then use some Access macros to import the .txt files. If splitting this action in two does not solve the problem then I will likely try the first of your suggestions since that also makes sense to me.