Carbing mead without a keg/co2 system can be difficult.
1) There's the potential that the yeast have reached their max potential, or may be too stressed out to continue carbing. We'd need some specifics about the gravity readings of the mead, abv, what yeast you used, what the FG was at the end, etc. You may need to use a bottling yeast (champagne) if the yeast you used to ferment is over it's alcohol tolerance. Of course, the issue here is that the high ABV toxicity is not a good environment for new yeast, so you may need to build up a starter to get that new yeast acclimated to a higher abv environment. If you've used sulfite/sulfate to try and keep it sweet, I figure you're pretty well stuck.
2) You can't carb sweet mead in the bottle reliably. If there's residual sugar and the yeast are still able to eat and carb, there's likely enough sugar to bottle bomb and nobody wants those.