The development and refinement of the crossbow was limited by the introduction of firearms, otherwise some notable improvements recently developed by hunters and hobbyists might have made it into the medieval arsenal - chiefly: the bolt retainer. This simple grommet-like thing is typically mounted in a small guard over the bolt channel and applies a very light bit of force to keep the bolt from falling out without significantly putting any drag on the bolt when fired. More advanced versions would release such pressure entirely on firing.
The stress on the bow, string and stock still can be an issue unless all are made of steel (perhaps with steel cable for a string) if the bow remains cocked for more than an hour. Even with steel, the forces will eventually cause failure, but likely not for a few hours.
In the later stages of its development the light crossbow was improved for use from horseback, with bolt retention and a levered or ratchet cocking mechanism that allowed loading with just one or two hands (no feet or braces required). So, even in real-world terms, the more advanced medieval crossbows were more than capable of vigorous movement while loaded.
Even without these advances, carrying a crossbow loaded and at the ready while moving for a few minutes is trivial and should not be prohibited.
However, any activity requiring the use of hands between loading and firing should be considered an interruption requiring a reload. With a light or hand crossbow that features a retainer and a good metal firing mechanism, the use of one free hand for other purposes should not cause an interruption. A heavy crossbow is so heavy and awkward that it requires two hands to carry in the ready position while moving.
If one wants to get picky, one might rule such convenient features as a retainer or steel firing mechanism are present only on a masterwork crossbow of the same type, but that would be a stretch and would depend largely on the general martial technology of the setting.
Here's a nice article about such things: http://www.huntingsociety.org/CrossbowDesign.html
Note in this article the interesting bit about Chinese repeating crossbows :)