Symptom:
When trying to ping from the ASA the next hop IP, ping fails if packet size is bigger than 1020 Bytes.
ASA# ping 10.48.66.1 size 1020 r 1
Type escape sequence to abort.
Sending 1, 1020-byte ICMP Echos to 10.48.66.1, timeout is 2 seconds:
!
Success rate is 100 percent (1/1), round-trip min/avg/max = 1/1/1 ms
ASA# ping 10.48.66.1 size 1021 r 1
Type escape sequence to abort.
Sending 1, 1021-byte ICMP Echos to 10.48.66.1, timeout is 2 seconds:
?
Success rate is 0 percent (0/1)

ASP capture shows:
  32: 09:48:00.900145       10.48.66.1 > 10.48.67.8: icmp: echo reply Drop-reason: (security-failed) Early security checks failed
  ...
  50: 09:48:02.890945       10.48.66.1 > 10.48.67.8: icmp: echo reply Drop-reason: (security-failed) Early security checks failed

Conditions:
The root cause is ASA Basic IPS signature 2151:
ASA# show ip audit count | in 2151|COUNTERS
IP AUDIT GLOBAL COUNTERS
2151 A Large ICMP                 15
IP AUDIT INTERFACE COUNTERS: OUT
2151 A Large ICMP                 15