Let's take a look at what you can do :
- Best solution : get a Eul's scepter ! As soon as Borrowed Time is triggered, Eul's him and he wont be able to regenerate thus using his ult for nothing. Many Abaddon will go in the melee thinking they are "unkillable", this will make them think twice before doing it again. You can obtain the same result with Astral emprisonment (Outworld Devourer), Disruption (Shadow Demon), Nightmare (Bane), Song of the Siren (Naga), tornado (Invoker) and Wind brewling's Cyclone (Brewmaster)
- Axe's Culing blade overpass Borrowed time. Borrowed Time triggers at 400 or less HP while Culling blade at level 11 insta-kill a target below 450HP (small margin) and 625HP at level 16 (better margin). Give that Abaddon some taste of Axe's axe
- Abaddon is reliant on mana to cast Apotic shield : diffusal blade on your carry or any mana burning spell will help you.
- Abaddon as a melee carry doesn't have a great disable (Such as Void or Alchemist) or a great chasing potential (such as Magina, Phantom Lancer or Mortred) so slowing him and kiting him in a teamfight is really easy. Get a support with a powerfull slow (Tuskar, Venomancer, Crystal Maiden etc.) or do it with an item (Rod of Atos, Skadi). Abaddon is not that great of a damage dealer,if he uses a bkb to prevent slow : just kite him or back a little then fight once he's no longer magic immune.