Does yeast age affect bottle conditioning?

I'm not sure if this is a dumb question but if I leave a batch in the fermentor for an extended period of time, like a month or more, does it affect the yeast's ability to create CO2 when I use priming sugar in the bottles? is there a prime time to bottle? Do the yeast crap out after a while? I've read a lot of posts about people aging beers for a long time but i wasn't sure if they may be force carbing or something. Just something I've been curious about, since I'm new and really enthusiastic about the hobby my batches so far have been bottled at about the bare minimum. Hard to be patient when you don't have a good pipeline of homebrew but I do a lot of traveling with work and can be out of town for a month or more at a time sometimes and I've been a little worried I might get sent out at an inopportune time during a fermentation.

I used to travel all the time for work - I'd make a batch, put it in my temp control device, and come back to it a month later - that was my "normal" mode of operations.

A month, even two is fine -
6 months sitting in a fermenter might have some very sleepy yeast and take a bit longer to carbonate.

If it's under 6 months, than no.....The yeast is plenty active to do the job without needing to add any more.

Temp and gravity are the two factors that contribute to the time it takes to carb beer.
Everything you need to know about carbing and conditioning, can be found here Of Patience and Bottle Conditioning. With emphasis on the word, "patience."

Last summer, I brewed a Double Imperial IPA. Because of the amount of hops, and the high alcohol content, the finished beer was very inhospitable for yeast. I ended up waiting 6 weeks to transfer the beer from primary to secondary, and then another month before bottling.

At 80*F, It took about two months to carbonate to a level that I found acceptable, but it definitely got there eventually. Unfortunately, IPAs aren't meant to be stored for that long, so the final product was maltier than I intended, and had just a hint of staleness to it.

My schedule has been hectic, so the same thing happened a few months ago. This time around, I added a half a packet of rehydrated Safale US-05 at bottling. All the bottles were carbed in a week.

It might not be necessary, but it won't hurt. It also made me feel more comfortable. And it certainly didn't affect the taste at all. Just something to consider.

cool guys thanks for the response, I've been reading a lot on the forums and hadn't seen this issue before. Was just curious and knowledge always helps me not to worry, its the unknown that I'm afraid of