The power control will not affect your SDCCH assignment success.
Exactly, how much is your “SDCCH ASSIGNMENT FAILURE RATE” ? (in average for your GSM1800 cells)
Regarding other answers, i’ll have to study which timers are used during this phase. To simplify the problem:
your BSC is getting a “CHANNEL REQUIRED”, then sends a “CHANNEL ACTIVATION” to the BTS, then receives a “CHANNEL ACTIVATION ACKNOLEDGMENT”.
Next step : the BSC is sending the IMMEDIATE ASSIGNMENT COMMAND, directly to the MS.
It is at that point that you measure a failure : the MS doesn’t answer the assignment command, or, if it does receive it, it is the BTS that doesn’t receive the SABM from the MS.
If messages are not received, it means either the BTS or the MS stop listening… so there might be a timer expiry. Check T3122 / T3120 / T3101… those are the timers that are quite obvious, but there might be additional timers somewhere… I’ll look for it when i have more time. But i think you can quickly find your answer about timers in the 3GPP documentation.
Check 3GPP TS 04.08 “mobile radio interface layer 3 specifications”, especially the chapter 3.3 “RR connection establishment”.