Question

Till when the eNB-S1AP ID is stored in the MME? and till when the MME-S1AP-ID is stored in the eNB?

Answer 1

EnodeB and MME has S1-AP protocol which sits over SCTP transport layer and there are two categories of messages, one's are UE-associated and another one's are non-UE associated. 
As part of UE attach procedure following messages are exchanged eNodeB and MME.

eNodeB <-------------------S1-AP-------------------> MME
1. "Initial UE Message (attach request)" , from eNodeB to MME (Mandatory).
2. Downlink NAS transport "Identity Request" from MME to eNodeB (Optional).
3. Uplink NAS transport "Identity Response" from eNodeB to MME (Optional).
4. Downlink NAS transport "Authentication Request" from MME to eNodeB (Optional).
5. Uplink NAS transport "Authentication Response" from eNodeB to MME (Optional).
6. Downlink NAS transport "Security Mode Command" from MME to eNodeB (Optional).
7. Uplink NAS transport "Security Mode Complete" from eNodeB to MME (Optional).
8. "Intial Context Setup Request (attach accept)" MME to eNodeB
9. "UE capability Info indication" eNodeB to MME.
10. "Initial Context Setup Response" eNodeB to MME
11. Uplink NAS transport "Attach Complete" from eNodeB to MME.

hope that help