How secure is HMAC SHA256
As I have a new hash every 3 second, it's easy for everyone to collect a big numbers of hash.  And as the difference between every UUID is always 3000 ms, maybe this could make it easier for the hacker to crack the key.


You might be reassured to read up on the security requirements that MACs are designed for.  Chapter 9 of the Handbook of Applied Cryptography is a good, freely available source.  (Section 9.2.2 is the most relevant.)

But to make this short, good MACs are expected to resist adaptive chosen text attacks, where the attacker doesn't just see the tags, they get to:


Choose messages of their own liking;
Cause you to compute these messages' tags;
Pick messages based on what they learn from earlier ones.


A MAC is considered broken if an attacker in that scenario can learn enough to successfully forge tags for other messages than the ones they caused you to authenticate.  That's a scenario much, much more adverse than the one you describe, where they only passively see tags (and no messages).  

So as long as you can keep the key secret, you probably have much bigger security concerns than this.