tuning stability depends on several factors. First thing to consider is, when using locking tuners, there is no need to loop the string round the machine heads. Pull it tight through the machine head and then lock. Looping the string makes the locking machanism irrelevant, and of no benefit.
Next would be to consider how well the guitar is setup. Is the floyd or trem in 'zero' position? Is the nut well cut? There is not really a need for locking machine heads most of the time, esp. if they guitar is well set up.