When you initially activate your phone, your SIM card is programmed during the activation process to tie your phone number to that SIM card.  So, your phone number, the SIM card and the IMEI (your phone's serial number) all work together as partners and together they work with the carrier's switch, to operate your handset and process your calls. 

So, if your phone is ever "deactivated" , the carrier's switch will take the phone number and assign it to someone else.  Therefore, splitting up that partnership between your SIM card and the phone number.

Therefore, in order to make a new connection to a new phone number, you will need a new SIM card as the old SIM card cannot be reactivated with a new number because it was already activated previously with the original number.  It only recognizes the original phone number from the original activation.