It's completely normal for business to slow down around the end of the Summer! This makes sense if you think about it, since most families go on vacation over the Summer when their kids are out of school. Business should pick up again for Thanksgiving, Christmas, and New Years Eve. Should you choose to work those Holidays, you'll be able to charge Holiday rate, which will hopefully help make up for these slower months.
In the meantime, if you're not getting any hits at all, you might try dropping your rate temporarily. Another option would be adjusting your availability to include some weekdays. When I first started on Rover.com, I worked a day job (6 hours/day Mon-Fri). I was surprised to find that many clients were comfortable leaving their dogs with me even though I worked outside of the home. The best requests to book would be for dogs that are already accustomed to being home alone while THEIR owners are at work. Pups of this sort are likely to be kennel trained and housebroken, which also makes things easier.
Now if you can just snag a couple repeat clients that go out of town for work EVERY month, you'll be set! Do your best job, be as available as possible without taking on more than you're comfortable with, and before you know it you'll have a great group of repeats that even book during slow months.
Best of luck!