In 2003, my husband was driving home with our children when he was involved in an accident. Our car was hit in the side by a driver that went through a stop sign while attempting to cross the 2 lane street. My husband had no controls on his street (no stop sign, no light). We only had one car at the time and had to rent while our car was being repaired, which cost us $1100.
I've sent 3 copies of the rental receipts to the other drivers insurance company, as recently as last month, and still haven't been reimbursed. They've claimed they never received them.
Is there any statue of limitation for reimbursement for rental car expenses? Although a significant amount of time has passed, I am still entitled to the money, right?

I am sure there are SOL on filing a law suit on a property damage claim but it will vary on the state this occurred at. I have to ask why you did not file a claim against your insurance ( if you had full coverage or rental car,) and just let them worry about getting the money.
Or file a law suit sooner when they did not settle.

But now that they have it, follow up every few days, record who you talk to and when.

At the time of the accident, we did not have full coverage only basic liability. For that reason repair costs and other expenses became our responsibility (since we didn't even have collision) My husband received a small amount of money from the other insurance for a back injury he sustained, but I don't believe the rental expense was included in that.
We were living in NY at the time of the incident.