What is the feat that prevents an spell-like ability from being dispelled from while in the presence of an antimagic field or when hit with a dispel magic/counterspell?
You may be thinking of Supernatural Transformation. This converts one of a creature's innate spell-like abilities (where 'innate' means 'derived from their race, type or subtype') into a supernatural ability. Supernatural abilities are not subject to dispel magic, but may still be suppressed by an antimagic field.
I'm unsure of the exact text, (I'm pretty sure it's not an OGL metamagic/meta-ability feat) but the idea of it is that it prevents dispelling. Supernatural Transformation might be right, but i'm still unsure.