Is there any constraint about connector's running time?

Im developing the custom source and destination connector. and using K8S deployment.

I have a question about connector having long processing time.

Assuming that source and destination process having long processing time, is there any policy or mechanism shutdown forcefully like timeout handling?

Yes, see env variable https://github.com/airbytehq/airbyte/blob/4e6380d2564f76dc86c909d53013db87cc2a3691/.env#L64 the timeout is configured to 3 days.