Below are the steps which you can perform to check issues about long running transport requests.
1. Go to SE38, execute the report RSTPTEST. It tests the tp status and STMS configuration check.
2. In STMS_IMPORT transaction -> in menu click on Goto -> tp system log .. this will give you if any error is there .
3. Check in SM37 whether RDD* jobs are running or not. If not, schedule them and import of the transport again.
4. Check in SM13 whether update is active or not as sometimes the update gets into error. If it is not active, activate it
5. Check in SM50 if all background workprocesses are in running status and there are zero waiting BGD processes. If so, you will need to wait for the free background workprocess to run RDD* jobs to complete the import of the transport.
6. Check if any of the filesystems (like sapmnt, oraarch etc) of the Central Instance, Database and application servers is 100% full. If so, please add necessary space.