I am working on a MFC project where I need a separate loop that will run continually or once every few seconds, and each time it may or may not need to run a Dialog to get some input from the user. I was thinking of using AfxBeginThread, but from what I have read about it, it doesn't really work with a continuous loop.
Don't do it. You can't just rip dialogs off in worker threads. They can only be started in the main thread, because they need the message pump in order to function.
If all you want is a signal of some kind that fires every few seconds, then what you want is a timer. Set the timer for the timer period you want, and when your main thread processed the desired WM_TIMER message, you can pop up a dialog and do your thing.
If you want your worker thread to do some work, which may or may not include asking the user for information, then you'll want to look in to having your thread use PostMessage() to send a message to the main thread, process that message int he main thread by asking the user for data, and then sending a signal back to the worker thread with the input data. One way to accomplish the last bit is by calling QueueUserAPC() from the main thread with the worker thread's handle and a pointer to a function that does somethething with the newly-entered data.