Arthurdent1949, there is another question. Normally, Access doesn't have this problem. We HAVE seen it before, but it isn't so common as to be an everyday occurrence. Usually when this occurs, you are doing something else before you do the CLOSE or C&R operation that triggers the problem.
Now the answer you didn't want to hear... technically, no, you cannot increase the system resources. They are not permanently allocated to you or your process. They are part of a pool of resources that you can draw from, and you have as many as the system has (unless you are on a server and are sharing with other users). On a single-user system, you have everything there is. So no, you cannot increase the resources. That's the bad news. The good news is that technically, that error doesn't always mean "system resources" in the literal sense of what you see when you do a web search for definitions of system resources. It can also mean that something failed when you tried to allocate something that indirectly involves system resources - like file handles, for example.
Windows allows you to do some sneaky things with buffering and lock management, as suggested by Colin. Do the searches he has suggested, as the most common causes of the problem involve sloppiness involving file management.
Without knowing more about what that DB actually does, it would be hard for us to give more closely targeted advice.