I have a 3-step process for when things like this come up when playing. Maybe it will be helpful:
Step 1 Re-Check the Rules: Make sure you didn't miss something; look for relevant entries in the rule book that might reference the area of gameplay you are in.
Step 2 Common Sense: When the rules are not clear, look for "the spirit" of the rules. Generally there's an intent behind the rules that can be gleaned from similar rules/abilities. If something feels too strong, it's probably the wrong idea.
Step 3 Logical Houseruling: If you are still without a clear answer (don't worry, this step happens a lot with Descent!) break it down with "real-world" logic, and then temper it with "game-world" balance. My process for this instance looks like this:
The ability refreshes once per round. A round is defined within a combat setting, Heroes move, OL moves. Since a round of combat is fairly quick (moving 4 steps, swing a sword once; doesn't take but a few seconds), it stands to reason that the ability does not take a long "period of time" to recover. Now, what are we talking about while traveling? Moving great distances, which would take a great deal of time. So it stands to reason that the ability would refresh between each "node" of travel.
Logical breakdown conclusion: Ability once per card.
However in actual gameplay you may find that this is too strong (I don't know, haven't gone thru this myself). If so, perhaps temper the frequency to require 1 travel period of "rest" before using it again. IE: If I use it on my 1st traveling node, I must not use it on the 2nd, and it will be ready on the 3rd.
Official ruling would be great, of course. But until then, I hope this is helpful.
I want to make sure that you understand I appreciate your feedback up front. It does, however, make we wonder if you play FFG games much. If you do, then you should know that the number one thing you never do with their games is start to guess the "intent" or "spirit" of a thing.
I have played their games for so many years, and have seen them come out with FAQs ruling first one way, and then changing their minds in the next update, that to guess their intent is never a good idea.
In this particular case, there are no rules one way or another, I seem to play with more lawyers than anything else, and I play with people who love debating. A very bad combination with as loose as FFG's terminology is, their poor consistency, etc.
Never the less, you make some good points. For now, pending any official ruling, we are allowing Arvel to use her reroll ability once per travel stop. I have been keeping track during the campaign, and it has amounted to a complete wash.