I am using the same gauge .. I read this guide on jemsite on how to change strings..:
Remove the high-E, replace with new string. Tighten the string at the bridge, leave the nut unlocked. gently pull the string at the 12th fret to stretch/bend the string and seat the string at the post. Retune and stretch/bend. Repeat 3-5 times until the tuning holds fairly well.
Remove the B-string, replace with new string, stretch/retune as above. Now, after the B-string is tuned, retune the high-E. DO NOT CONTINUE replacing the G-string until both the E and the B are tuned. (disregard the other old strings).
Remove the G-string, replace with new string, stretch/retune as above. Now, after the G-string is tuned, retune the
higher strings one at a time. DO NOT CONTINUE replacing the G-string until both the E and the B are tuned. Note that I tune the G, fine tune the B, fine tune the E, recheck the G, fine tune the B, fine tune the E, recheck the G, etc.. until all 3 are finely tuned. (disregard the other old strings D-A-E).
Remove the D-string, replace with new string, stretch/retune as above. Now, after the D-string is tuned, retune the higher strings one at a time. DO NOT CONTINUE replacing the D-string until the D-G-B-E strings are tuned to pitch. Use the same repetitive manner as above. Remember if you fine-tune ANY string you must check all others for proper tune.
Remove the A-string, replace with new string, stretch/retune as above. Now, after the A-string is tuned, retune the higher strings one at a time. DO NOT CONTINUE replacing the A-string until the A-D-G-B-E strings are tuned to pitch. Use the same repetitive manner as above. Remember if you fine-tune ANY string you must check all others for proper tune. HERE IS WHERE IT GETS REPETITIVE and tedious... but keep at it. It will pay dividends later.
Remove the low E-string, replace with new string, stretch/retune as above. Now, after the A-string is tuned, retune the higher strings one at a time. Remember if you fine-tune ANY string you must check all others for proper tune.
Now, I didnt string my guitar this way.. I just went from bottom E to high E one by one... I did stretch them though.. If this is my problem I am curious because that is how I strung my RG520 and I never had any problems with it holding tune..