Should I sell my fledgling, struggling franchise territory, hire someone to run it or shut my doors?
As to which of these options might be best, that depends on your situation. Going in reverse order, I would only shut my doors if I believed that the franchise is a loser that I had no chance of turning around and that, realistically, no one would pay anything to buy it from me.
Assuming that the business potential is solid but that you simply don't have time to build it yourself, then hiring someone else to run it and make the business successful is a good option. Be aware that this strategy might accelerate your losses in the short run because you have another salary to pay. But if the person you hire turns the business into a money maker, you can either keep it or sell it much more easily for more money at that point.
The other option you mentioned is selling the business right now. That may well be the safest option from a risk standpoint, but it is often fairly difficult to sell a "fledgling and struggling" business. Most buyers of businesses want to buy something that is successful and then make it even more so after they own it.
I'd suggest discussing these options in detail with your franchisor and asking what, if anything, he or she can do to help you in your present situation. Hope that helps and good luck.