@Bhishan It's extremely unusual for Alfred to shut down like this, so I'll need quite a bit more info to work out what could be happening on your Macs.
1. Could you provide any crash logs shown in Console.app (User Reports from the left hand list).
2. Is there any pattern to what you're doing, for example, a specific workflow you use in the run up to this issue.
3. Do you have any unusual configuration on both your Macs (apps which may change lower level Mac configuration such as "auto cleaner" apps).
Cheers,
Andrew