sp_databaserestore: "stopat" gives error "no database backup found"
I don't think the problem is with sp_DatabaseRestore but there are alternatives as you can see on this question (includes the script):

How do I create an automated SQL Server restore script for multiple backups?

Before you run your restore:

1) you must check that all your backups exist in the server

2) you must check the total disk space required by the restored-to-be-database is available on your drives 

3) who is currently using the database - you will need exclusive access to it, if it already exists

4) I also save synonyms, triggers, indexes and permissions before I do the restore, so that I can re-apply these things later on if I need to.

5) questions for you:
Are you using the WITH MOVE option to ensure the database files are allocated to specific drive(s) / mount-points which have enough free space?

Also, look into the use of WITH RESTART for your restores...

The backup or restore was aborted - what could it be?