That’s not quite right.
Got answer:
HEADER:
opcode = QUERY, id = 41, rcode = NXDOMAIN
header flags: response, want recursion, recursion avail.
questions = 1, answers = 0, authority records = 1, additional = 0
QUESTIONS:
s2.(mine).net.(mine).net, type = AAAA, class = IN
AUTHORITY RECORDS:
-> (mine).net
ttl = 1080 (18 mins)
primary name server = ns2.(mine).net
responsible mail addr = root.(mine).net
serial = 2024052901
refresh = 3600 (1 hour)
retry = 3600 (1 hour)
expire = 1209600 (14 days)
default TTL = 1080 (18 mins)
Got answer:
HEADER:
opcode = QUERY, id = 43, rcode = NOERROR
header flags: response, want recursion, recursion avail.
questions = 1, answers = 0, authority records = 1, additional = 0
QUESTIONS:
s2.(mine).net, type = AAAA, class = IN
AUTHORITY RECORDS:
-> (mine).net
ttl = 1080 (18 mins)
primary name server = ns2.(mine).net
responsible mail addr = root.(mine).net
serial = 2024052901
refresh = 3600 (1 hour)
retry = 3600 (1 hour)
expire = 1209600 (14 days)
default TTL = 1080 (18 mins)
Here you have an NXDOMAIN (because of the searchpath giving a bad domain name) and a NOERROR (because there’s no AAAA record for that server). Both come with a ttl of 1080, i.e. should be cached for that long.
Even completely bogus names come with a ttl (and refresh, retry, expire):
Got answer:
HEADER:
opcode = QUERY, id = 49, rcode = NXDOMAIN
header flags: response, want recursion, recursion avail.
questions = 1, answers = 0, authority records = 1, additional = 0
QUESTIONS:
doesnotexist, type = AAAA, class = IN
AUTHORITY RECORDS:
-> (root)
ttl = 86382 (23 hours 59 mins 42 secs)
primary name server = a.root-servers.net
responsible mail addr = nstld.verisign-grs.com
serial = 2025052801
refresh = 1800 (30 mins)
retry = 900 (15 mins)
expire = 604800 (7 days)
default TTL = 86400 (1 day)
The only case when there’s no caching data is when the nameserver cannot be contacted. I’m not sure what the nameserver replies when it’s alive but has no internet—I’m not taking down my connection to test that edge case. 
PS: So, if those AAAA NXDOMAINs are not cached, then either those domains have tiny TTLs, or something is wrong with the lookup provider implementation.