Email inbound process is done by user SAPCONNECT so that you cannot debug it via normal debugging approach.
then you have to follow the steps below to debug:
1. Inside one entry like below into table BCSD_BREAKLOOP.
BL Module = INBOUND
CREATEDFOR = SAPCONNECT
Set the expire time accordingly.
Note: As the insertion of this entry will lead to an endless loop in SAPconnect inbound processing, please make sure to delete it or set the status to abap_false.

2. Send your mail to agent inbox mail box as usual, then go to tcode SM51, you should find the endless loop there.
Click Administration->Programm->Debugging:

This is because your entry inserted by step1 takes effect:

3. In debugger, use Shift+F12 to jump out of the endless loop manually:

After that you could debug the left inbound process of SAP connect now:
