A decent LiPo charger, one with a balance function, will usually also have a safe discharge function which takes them down to just above 3V for storage. Better ones, such as iMax B6 and Turnigy Accucell 6 (the same machine in different boxes), have both a Discharge & Storage charge/discharge function, which first discharges the battery and then recharges it.
As far as I know, that function is only intended for use with LiPos when they are to be stored unused for 6 months or so. If they are believed to be damaged you can do a Storage then Charge cycle several times and doing so can 'invigorate' the chemical reaction which makes them work. Bear in mind however that all rechargeable batteries have a finite limit to how many times they can be charged/discharged.
As far as I know it is not necessary to discharge LiPos before charging them when in normal use, but a healthy LiPo should hold around 4.2V fully charged so, if this should start to drop while the battery is still relatively new/virginal, say less than 6 months regular use, 12 months light use, then it may be that it is suffering from one of several problems which used to plague 1st Gen LiPos which, we are told, have been ironed out by design improvements since. In this case I'd also run the charge/discharge cycle a few times and see if it improves matters.