Think of your markers as a q tip. When inking up stamps you'll want to ink in one direction or else it get fuzzy, like a q tip going back and force. The marker is made up of fibers.
I also like to store my markers lying down but if one end starts to dry out, just stand it on end as the ink runs to both ends.
To reink your markers, you might want to rest the tip over your stamp pad and just add some drops of ink refill and I'd suggest doing it before it gets frayed or dried out. Check out the tips.