A family of Microsoft relational database management systems designed for ease of use.
Okay, so now I am even more perplexed, and pleased too, as the 'Cannot open any more databases' problem has stopped. I have set the trusted folder for the front and back ends, repaired Office 365 for the third time, checked all my code for spurious 'CurrentDb' objects not being set to Nothing (I found two instances and corrected them before recompiling and saving) and have rebooted my pc again. After all that the problem has not reoccurred so have I sorted it, I am not sure, but am happy to plod on with a working environment now.