Mariculture's Air Pump provides extra air to players underwater within 64 blocks, provided it has power. It does this every 300 ticks by default, which translates to 1.5 seconds normally. It seems to be slowed slightly even in populated chunks on this server, taking long enough to refill that the player's air supply is already depleted, and is even slower when you are not in its chunk, due to the slowdown effect that occurs. Can the I:"Air Pump > Ticks Between Supplying Air"= config line in Mariculture's machines.cfg be reduced, since the tool is rarely used due to its niche.
I think it may have been a little below that, the lowest I've seen today is 16 tps, however, and that still shouldn't be enough of a reduction to allow the air supply to completely drain. Just to note, the full diving suit is already being worn, so air is already used at a reduced rate.
Can you test it in singleplayer too? If there is the same issue please try to find out a good tick rate, which is not too low and still works.
In single player, it takes just under a full bar of air to refill. This is probably a little slow, so setting the tickrate to something in the region of 75-150 should solve the issue without using too many resources.