Spiderling counterattacks are the culprit. :)

Part of the spiderling skill descriptions, but since you can't see those in-game (to my knowledge), they really should move it into a passive for the boss instead.

The above is correct. To be clear, any time the spiderlings get a CA they heal Agreth by 10% Max HP, which is a huge chunk. Here are their skill descriptions:

Nether Spiderling Skills (4 Minions)

• Juvenile Venom [ATK] Attacks all enemies. Places 5% [Poison] debuff for 2 turns. Cannot be resisted or blocked. (Damage Multiplier: 2 ATK)
• Mother’s Grace [Passive] Heals Agreth the Nether Spider by 10% of her MAX HP each time this Spiderling counterattacks. Places [Ally Protection] buff on Agreth for 2 turns whenever a [Counterattack] buff on this Spiderling is removed or expires. This [Ally Protection] buff cannot be removed. If Agreth already has an [Ally Protection] buff, increases the duration by 1 turn instead. 

That makes sense, thank.you. :)

Unlike the dungeon Spider, wich is immune to heal reduction, you can block the healing on Argeth with the heal reduction debuff. Especially nice if you have Geomancer, burn the big Spider and make some minor AoE attacks to get hit by all Spiderlings.

It seems weird, but I only have this problem when I put Nekmo on my team. 

because of the huge detriment that comes from the spiderlings' counterattacks, the default ai is for champions to not use their aoe attacks while fighting agreth. in nekmo's case however, that's not possible.

Ah, yes, you're right - all of Nekmo's attacks are AoE!