Regen is intended to slow in combat, and that includes Stamina and Mana (haven't tested health but would assume so).
Mana regen gear DOES work in combat, its been tested, I've tested it myself.
It takes something like 90 seconds (in combat) to fill a full mana bar at base rate.
If you have a higher mana pool you will regen more mana per second than if you have a small mana pool because it regens 1.1% of your mana pool per second at the base rate. 1.1% of 100 = 1 per second or 1.1% of 500 = 5 per second.
If you are wearing +100% regen your manabar will go from empty to full in combat in 45 seconds (2.2% per second).
+200% regen will fill an empty manabar in 23 seconds (4.4% per second)
Also mana regen pauses while your casting if your maintaining a spell, or simply holding one ready to fire your mana will not regen. This is intended, it represents the concentration required to focus on the spell.
If your having mana issues you need to aproach it from 3 angles.
Reduce your spell costs (obviously) with gear/perks
Increase your mana pool - Because regen is % based you will be regenerating more mana per second if you have a higher pool.
Directly increase mana regen - It DOES work in combat.
If your still having problems, try this potion in combat, It will give you upfront mana and supercharge your regen in combat or out of combat:
Spoiler
Jazbay Graqes + Red Mountain Flower + Firesalts
Curently These potions I'm making at about 60 alchemy + perks =
+70% Mana regen (300 sec)
+56 Magicka pool (60 Sec)
Restore 88 Magicka