BoT gives afflictions to some units and kills others. It hurts anyone using non-undead armies, and especially badly anyone who uses expensive troops... I don't know does magic resistance affect it, or magic scale, or anything like that. I'd say that Ulm is hurt badly, but as you are too you should try to get rid of it.
You can either research Thaumaturgy and cast Dispel or fill the Global pool with your own Globals. You would need five, though, and I doubt you ca cast that many...
If you can reach Enchantment 5, and have someone with 5 Nature, you can try Gift of Health. This will let your units heal afflictions, and give them more HP, so you won't suffer as much.
But, overall, Burden of Time is bad news. And what's worse, the AI don't seem to try to dispel it, even those that suffer from it.
It may be rare, but the AI does sometimes dispel Burden of Time. I wouldn't count on it, though. You could also assassinate the caster. Likely the caster is in the enemy capital. Can be hard to do, though. (Assassins, fires from afar, seeking arrow, surgical strike, etc.).