Almost every MANPAD uses an IR seeker, not radar. The A-10 engines are mostly hidden from the ground, inside a wrap-around tail. There are few angles from which the exhaust can be seen. It is in fact a very simple form of stealth. The aircraft turns of course, changing the view and causing simple heat seekers to loose the aircraft. Of course, the aircraft also carries flares and other decoys, and it can be accompanied by a Growler.
If the A-10 does get hit, it will probably be fine. It has quadruple-redundant controls. It can fly with the loss of an engine, half the tail, and 2/3 of one wing. MANPAD explosive charges are small. The A-10 engines are spaced apart from each other, making it unlikely that a hit on one engine could disable the other. Experience shows that the aircraft is tough: they often return to base after getting hit by a missile even larger than a MANPAD, such as truck-mounted Russian equipment.