Hi. Sounds like your place is in good shape so it's nothing on your end. You shouldn't have trouble finding a qualified tenant. Yes, definitely get a non-refundable deposit if allowable so that they don't just string you along while they weigh their options. If they are running late -- that usually translates to we are looking at another place right now.
Just had a showing yesterday. I made it clear on the phone what the terms are in order to move in, first month's rent + 2 months deposit (among other things). They said no problem. So they look it over and like the place (what's not to like!) then they start telling me my ad says only 2 months due. NOPE, I know what my ad says... it's been the same for years... I just tweak it a bit as needed and update the photos. They also did not want to pay the application fee for TurboTenant. Not off to a good start.
Perhaps the folks you showed it to didn't qualify or didn't have enough for the deposit, etc. At least they showed up! I've had one too many not show up and not even bother to tell me. Hey, just tell me you found something else... save me the trip out there. Sadly, you will soon find out that most of them are inconsiderate and liars, too. Hang in there!