Why availability group resource goes offline in WSFC?
Seems it's your follow-up question of this.. Hope you got root cause of the issue using FailoverDetection tool. Perhaps the cause could be from either Internal Health Issue or system wide issues as detailed here...

Why is that happening?

As you found in error log, the AG trying to take recovery actions, as part of that either AG resources could fail-over to new primary replica as AG is determined unhealthy and will report failures on IsAlive calls, or if the quorum lost, resources goes offline.
Further reading on lease-time and health-check timeout

If one of the cluster networks is down, then the cluster role goes to offline state?

Yes, if the quorum lost.
For instance, if the WSFC formed with 2 nodes (total 2 votes), to have quorum to be healthy, always more than half of the quorum vote nodes to be alive. In this case if one node is down cluster resource may go off-line as the cluster consider to be unhealthy while there is 1 vote is not more than half of the total votes.
To maintain healthy-cluster, configure a file-share-witness (Node and File Share Majority), so that the quorum can have an additional vote from file-share to support the cluster to be healthy. If one node is down there will be 2 valid votes (1 Node + 1 File-share) out of 3.
In Summary:

If you found that the root cause is quorum lost, you may need to configure proper quorum mode.
If it's Network interface failure, consider having dedicated NIC for the cluster heart-beat communication (screenshot for your reference).
If the cause is aside from those two, you need further investigate to find bottlenecks of resource pressure in servers: some free-tools from Microsoft (Ref1, Ref2, Ref3), or third-party tools can help.

Multiple NIC for WSFC: