statute of limitations for health insurance to subrogate

I was in a car wreck in TX. My personal health insurance paid most of the med bills. My auto and the at fault party insurance paid a few med bills, and I got a large settlement after a few months.

How long does my health insurance co have to subrogate? So far they have not. Do they always subrogate?

I'm just wondering the "just ifs"

My policy (health care) is written in KY where I live. The wreck was in TX.

Thanks!