Checking /var/log/messages, I've found the following notification about blocking UDP port 67 out.
I actually went to CSF's configuration and allowed this port and the message was gone.
After 5 minutes I thought I might have risking my system without properly checking (though sounds like my server is the one which is blocked from sending data out), so I've removed the port from CSF, but would appreciate if anyone has any idea what this might be.
Jun 3 08:11:32 cwp dhclient[3102]: DHCPREQUEST on eth0 to 172.31.1.1 port 67 (xid=0x216d4be)
Jun 3 08:11:35 cwp kernel: Firewall: *UDP_OUT Blocked* IN= OUT=eth0 SRC=159.69.16.218 DST=172.31.1.1 LEN=328 TOS=0x00 PREC=0x00 TTL=64 ID=12990 DF PROTO=UDP SPT=68 DPT=67 LEN=308 UID=0 GID=0
Jun 3 08:11:35 cwp dhclient[3102]: send_packet: Operation not permitted
Jun 3 08:11:35 cwp dhclient[3102]: dhclient.c:2697: Failed to send 300 byte long packet over fallback interface.