Actually, there is no statutory requirement in Florida for any insurance company to respond to a third party liabiity claim in any particular time frame or even respond at all.
The insurance company is free to ignore your demand letter if it so desires. So, yes, it can just sit on the letters and at some point you are entitled to file a lawsuit against the other driver.
The general practice is that the liability carrier will respond to the demand letter when it gets to it, which could be in the amount of time it takes to get to it on the pile that it's in with all the other demand letters.
Depending on the backlog, could be 60 or 90 days, or even more. Could be less.
From my understanding if they don't respond in 30 days, then it is void. which means your offer is Off the table.
Absolutely wrong. And I'd like to know where you got that understanding so I can disabuse you of it.
The demand for X dollars is never void and is always on the table until the claimant rescinds it or the insurance company rejects it. And even if the insurance company rejects it, one can still use that amount as the basis for the lawsuit.