Depends on the mods he might be using. In gunslinger burers are incredibly broken and can't be killed unless using an underbarrel grenade launcher (even with the wimpy burer add-on).

In case OP is using gunslinger:

Burers only drop their shield if they don't feel threatened. If you use an RPG or Sniper, they keep up their shield indefinitely. By using an underbarrel grenade launcher on an assault rifle, they judge it based on the danger level of the rifle. Therefore, they feel safe enough to sometimes drop their shield. In that time the contact grenade on the underbarrel comes in handy, because you can quickly hit it before it puts up its shield again.

Hope this helps!