you should check your BSC’s
(all the cells of the network, or just one or few BSC’s ?)
if ALL the network, then it might be the MSC. Either a MSC board, or a timer that has been modified. The SDCCH is used for exchanging messages between MS and MSC. If it takes longer for the MSC to answer these messages, it might impact the whole network.
You could investigate the VLR as well. The VLR is taking part during the authentication. If the VLR is slower, it will increazse the length of the SDCCH, etc.
That’s a very interesting problem, please let me know how it ends !!