The rules for this are not entirely clear. The Flaw Grab-Based reads:
An attack effect with this flaw requires you to successfully grab a
target before using the effect (see Grab). This generally applies to
an effect that is close range, since you have to be in close combat to
grab anyway. If the effect’s default range is not close, apply the
Close modifier as well. If you do not succeed on the grab, you cannot
use the effect. If your grab attempt succeeds, the effect occurs
automatically as a reaction.
Example: Leech has a draining touch that is a Grab-Based Weaken
Strength effect. So the monstrous villain has to take a standard
action and make a grab first in order to use it. If his close attack
check hits, the target makes a Dodge or Fortitude resistance check
against Leech’s Strength. If it fails, the target then makes the
Fortitude resistance check against the villain’s Weaken effect to see
how much Strength Leech drains away.
This flaw is essentially a form of Resistible, with a grab check
rather than a regular resistance check (see the Resistible flaw for
(per the Grab-Based flaw on the D20 HeroSRD Modifiers page.
From that, we can take away two things:
- This follows the normal grapple rules.
- This is partially based on the Resistable flaw
If a power is Resistable, it is resisted separately each time you use it. That said, your target gets a chance to Escape (a move action) each round they are grappled, so it pretty much covers that aspect of Resistable.
In the end, as with most questions where there is no 'official' answer, I'd talk to your GM. For a game I was running, I would consider it sensible for the Grab to remain after the power fires (as long as it makes sense for it to do so - a Grab-Based Affects Others Only Teleport obviously wouldn't leave you grappling your target after a successful attack!) and permit you to continue using the Grab-Based attack each round without having to re-grab each time. If your target was successful in an Escape, of course, you would have to re-grab.