The extra information was very helpful. I looked the app up on the App Store and found this review:
Great App, but times out?
Wonderful app with a few glitches to work out. When im timing my chanting, i have to set my phone screen so it wont lock. It stops logging the time when that happens. Either that or keep touching the screen before phone locks. Id think the app would stay open while the timer is in use or the time would at least keep running. A little confusing to pay 1.99 for an upgrade & then asked to pay 2.99 again. Why not just make it 4.99 or 5 and call it a day? Otherwise I enjoy this app alot. NMRK
I wrote the above review 2 yr ago hoping theyd fix this glitch & they have not. I dont really use this app anymore bc the timeout/screen going black really affects my chanting (negatively), so i will continue with other chanting avenues. Really unfortunate as i otherwise like the app.
{Emphasis mine}
So, it would appear the problem is neither yours nor Apple's to fix, The fact the app has not been updated since 2013 and has no support link listed, leads me to believe the developer has lost interest in the project and is unlikely to fix it. My suggestion would be rather than wasting your time trying to troubleshoot the app, spend it looking for a replacement.

By-the-way, a search for "Buddhist Chants" on the app store turns up nothing for macOS, not even ChantBuddy, but there are fourteen apps for iPadOS and iOS.