If a Brutalizer is equipped and then detached, does the +2 persist on the unit?

No, the unit does not keep the +2 bonus when Brutalizer detaches.

As confirmed by FAQ #8582, when Brutalizer leaves the unit, all bonuses it provided (both the base +1 Might and the conditional +2) are lost immediately. Per Rule 136.3.a, a Might Bonus applies only while the card is Attached and stops applying as soon as it's no longer Attached. The same logic applies to Brutalizer's conditional effect — it's tied to the equipment being attached, not a lingering buff.