One of mine was refusing anything but live, and even that sometimes when I got him as a baby and by the time he was 4 or 5 months old is when I finally put my foot down and he went 6 weeks without eating until he finally gave in and took f/t. He didn't even lose any weight during that time and managed through it with no problems. I'd say by the time a healthy snake reaches a few months old it should be able to handle going that long without it causing harm.

But of course making sure they are at a nice plump weight, if feeding on live just fine, prior to attempting to push the f/t only approach for a long period if they keep refusing f/t is always the best idea, so you know they'll have plenty of weight on them to make it through the weeks if they choose to take that long to switch.
Attempting to fight it out with them like that if they are already on the thin side, or not quite "plump" for their age would likely not be a good idea.

One of my biggest successes with getting a snake to make the switch is a 14 year old bp. He had eaten live only for the first 8 years of his life and had refused f/t many times during that period. But using the method I mentioned previously I was even able to get him to switch after 8 whole years of him refusing f/t and only wanting live. He's been on f/t ever since. He was one of the unfortunate ones that ended up having one of those near death mouse attack accidents at the hands of an inexperienced person. But after surviving that it made me push for the switch that much harder.