Retracting the undercarriage in a circling approach is a sure way to finish up sitting on the runway the undercarriage retracted. The workload for a SP circling approach in real conditions is high, so why increase the workload any further. An engine failure in the circle with the gear down is no worse than one on final approach.
Complacency can be the root of all evil, trying to land a heavy twin with the gear up as Wally says gives the pilot so many reminders such as non normal power settings, hard to slow to flap speeds etc.
I am reminded of an incident where a newly endorsed PA31 pilot developed the habit of not putting the gear down until turning final. Wise words were given to him about putting the gear down downwind prior to turning base.
Our ace didn't listen and eventually had the occasion to shut a rough running engine down. Arriving in the circuit with 9 pax, he carried out his normal circuit and turning final selected the gear down. At 300' to his horror, the gear was still extending, the result, a very dodgy go around with the gear still trying to extendand then retract. As murphy would have it, the remaining engine had a weak hydraulic pump and more time was needed to get the gear down.
Most turbine aircraft have a gear warning on setting more than take off flap, if the gear is up.