Symptom:
The problem is with one of Firepower Management Center system processes requiring local hostname to be resolved via a DNS server.

In a very specific scenario, this may be causing policy deployment tasks to get stuck with in a "Task completed successfully" state, making further deployments to be impossible.

Conditions:
The following command can be used to verify if (and how fast) a Firepower Management Center can resolve its own hostname via a DNS server:
time nslookup `hostname`

Outputs like the following confirm presence the problem:
admin@FMCv:~$ time nslookup `hostname`
Server:		10.10.10.10
Address:	10.10.10.10#53

** server can't find FMCv.test.local: NXDOMAIN


real	0m0.158s
user	0m0.000s
sys	0m0.004s