Development partner using Presence REST-API to subscribe large number of users' presence status that cause Breeze server (V3.8.1) CPU to keep high usage and no response on presence status update. Presence Service release is V10.1.

We must to restart Breeze server to recover Presence Service, any advice to better manage Presence CPU resources to release unused resources regularly and keep CPU in a normal usage status.

This really sounds like an issue you should bring to the attention of the Avaya Support team (www.avaya.com/support).
How many Breeze servers in the cluster?
How many total subscribes does the application server do?
Are Breeze and Presence both on the latest release (Breeeze Platform is 3.8.1.1, Breeze Presence Services 10.1.0.0)?
Is the application inserting any real time breaks or does it just drop into a for loop and subscribe for 1000's of users presence status creating a firehose of requests?