Can Dancing Grenade be played indefinitely as long as I have power to pay?

Yes — as long as someone has [A] (1 Fury Power) to pay and there's a valid unit to target each time.

Here's how it works:

When Dancing Grenade resolves, it deals 2 to a unit, then the controller of that unit may play the card again from the trash for [A] instead of its normal cost (Rule 356.1.a — "for [Cost]" replaces the base costs). That new cast resolves, its unit's controller gets the same option, and the loop continues.

Each subsequent cast gains +1 Bonus Damage for every time this spell has dealt damage earlier in the turn. So cast 2 deals 3 (2+1), cast 3 deals 4 (2+2), cast 4 deals 5, etc. The damage escalates each iteration.

There's no "once per turn" or "only once" restriction on the card — the permission is granted each time the spell resolves. So the loop has no hard cap, only practical ones: running out of [A] to pay, or running out of units that can survive the escalating damage.