I can't remember the exact sector length but there was a cut off as to when they would retract the gear and when they wouldn't bother.
Actually the gear is probably not strictly required to be as strong as its longhaul partner if Boeing wanted to recertify them. Think about it....Much lower average takeoff but similar landing weights to the Longhaul variant. I believe the gear was probably optimised for short sectors - main issue here is brake temperatures as with frequent short turnarounds you still need the brakes to be cool enough for a max energy RTO on the next takeoff.
A Landing gear cycle is not defined with a landing/take off its is derived from Extension and Retraction. I.e. the landing gear mechanism being "cycled".
This is circa 2003 info as thats when I worked in Tech Services. They may well have changed the the policy by now but the Gear overhaul is an expensive cycle driven procedure. Any increased fuel burn on a short sector
will be offset by the reduction in frequency of Gear overhauls.
The specific 'numbers' will all be in some spread sheet somewhere which will examine the pros and cons of with/without winglets, with/without gear down etc. All to find the most "Financially Efficient" - not necessarily fuel efficient - way to operate the aircraft on any given route.