I've been out of martial arts for 19 years. At 34/5 I feel that I'll never be able to stretch as far as I could as a kid. Is this true, or can I work on doing that and getting stretchy and flexible again? I only have the time to attend one training session a week. I intend on practicing my art when I can at home, but what is there I can do in a restricted space to try and get fit and flexible again?
I have become more flexible now than I was when I was young. However, I was not very flexible then, and I'm not that much more flexible now. I can't do the splits, and some kicks are beyond my abilities at the moment.
I believe that working on flexibility is time well spent, but it's only part of the picture. Work on your cardio. Work on your balance. Work on your breathing. As you learn stances and transitions, practice them well on your own time. You need little space for these things.
One of the best exercises you can do for cardio is jumping rope. Period. It's a great exercise, and it takes nearly no space and only a simple rope in the way of equipment.
For balance, stand on one leg until you can do it as long as you wish. Then begin to move while keeping your balance. Balance is key to so much in martial arts.
Stances are also important, and IMHO are not practiced enough by anyone, including myself.
Breathing is something we all do of course, but conscious correct breathing from the hara is something you can practice - assuming your style of martial arts emphasizes this - I hope it does.
Flexibility can be gained by stretching exercises, as well as by practicing doing the splits. You can rig up a rope and a pulley on a doorway to stretch your leg muscles - only use your arm strength so that if you trip or lose your grip or whatever, you are not hung up in the air like a side of beef.
Dynamic tension builds muscle without weights or equipment of any kind. It's boring and difficult to maintain the mental concentration necessary to do it diligently, but it works for most upper body groups.
Situps build core strength.
Stair climbing is great for leg strength and kicks.
Nothing I have described requires much in the way of space or equipment. Just desire and time.