If keep using the same ObjectManager, will there be OutOfMemory?

I have a Web Service Application that uses Aurelius. I am wondering - if I keep using the same ObjectManager to serve Service Calls (that may run 24/7 continuously, with the back-end database keep having new thousands of records inserted on a daily basis), will there be any potential problem (like ObjectManager running out of memory)?

Does ObjectManager "Clear" itself in someway?

Yes, you will have a problem. The object manager is not intended to be global, or long-lived. You should create it for a specific use context, use it, then destroy it.