Quick sanity check - I've read through several related questions and I'm still confused about this topic.
I have build the app with a provisioning profile(in-house) with enterprise account. That provisioning profile is getting expired in next few days and the distribution certificate used for that provisioning profile expires in next year. If the provisioning profile gets expires will the apps which were distributed stops working or they will keep working as distribution cert is intact?
Your enterprise app needs to contain a valid provisioning profile. This means that it will need to be updated at least once every 12 months.
If your enterprise app is distributed by MDM then you can use your MDM to distribute a new provisioning profile without updating the entire app. A new app version will be required at least once every 2 years as the signing certificate will expire.
For more information refer to this 2014 WWDC session - Transcript
It was also covered briefly in this 2019 WWDC Session