I ran the dump twice, once against the member that responds properly (and it is in production so the dump may include activity from other clients) and once against the bad member.
.99 = my client PC
.142 & .144 = self IPs for F5
.147 = virtual server
.16 = good member
.153 = bad member
GOOD MEMBER
09:57:22.933063 IP XXX.XXX.XXX.142.37907 > XXX.XXX.XXX.16.http: S 3393865625:3393865625(0) win 5840 out slot1/tmm1 lis=
09:57:22.933674 IP XXX.XXX.XXX.16.http > XXX.XXX.XXX.142.37907: S 4287057984:4287057984(0) ack 3393865626 win 16384 in slot1/tmm1 lis=
09:57:22.933991 IP XXX.XXX.XXX.142.37907 > XXX.XXX.XXX.16.http: . ack 1 win 46 out slot1/tmm1 lis=
09:57:22.934074 IP XXX.XXX.XXX.142.37907 > XXX.XXX.XXX.16.http: P 1:8(7) ack 1 win 46 out slot1/tmm1 lis=
09:57:23.099200 IP XXX.XXX.XXX.16.http > XXX.XXX.XXX.142.37907: . ack 8 win 65528 in slot1/tmm1 lis=
09:57:23.604580 IP XXX.XXX.XXX.99.51251 > XXX.XXX.XXX.147.http: S 870178715:870178715(0) win 8192 in slot1/tmm1 lis=
09:57:23.604624 IP XXX.XXX.XXX.147.http > XXX.XXX.XXX.99.51251: S 1152696155:1152696155(0) ack 870178716 win 4380 out slot1/tmm1 lis=NOS_Test
09:57:23.604887 IP XXX.XXX.XXX.99.51251 > XXX.XXX.XXX.147.http: . ack 1 win 256 in slot1/tmm1 lis=NOS_Test
09:57:23.608355 IP XXX.XXX.XXX.99.51251 > XXX.XXX.XXX.147.http: P 1:106(105) ack 1 win 256 in slot1/tmm1 lis=NOS_Test
09:57:23.608397 IP XXX.XXX.XXX.144.51251 > XXX.XXX.XXX.16.http: S 3589583094:3589583094(0) win 4380 out slot1/tmm1 lis=NOS_Test
09:57:23.609020 IP XXX.XXX.XXX.16.http > XXX.XXX.XXX.144.51251: S 1971215146:1971215146(0) ack 3589583095 win 16384 in slot1/tmm1 lis=NOS_Test
09:57:23.609033 IP XXX.XXX.XXX.144.51251 > XXX.XXX.XXX.16.http: . ack 1 win 4380 out slot1/tmm1 lis=NOS_Test
09:57:23.609046 IP XXX.XXX.XXX.144.51251 > XXX.XXX.XXX.16.http: P 1:106(105) ack 1 win 4380 out slot1/tmm1 lis=NOS_Test
09:57:23.613151 IP XXX.XXX.XXX.16.http > XXX.XXX.XXX.144.51251: P 1:530(529) ack 106 win 65430 in slot1/tmm1 lis=NOS_Test
09:57:23.613194 IP XXX.XXX.XXX.147.http > XXX.XXX.XXX.99.51251: P 1:530(529) ack 106 win 4485 out slot1/tmm1 lis=NOS_Test
09:57:23.712861 IP XXX.XXX.XXX.144.51251 > XXX.XXX.XXX.16.http: . ack 530 win 4909 out slot1/tmm1 lis=NOS_Test
09:57:23.746385 IP XXX.XXX.XXX.99.51251 > XXX.XXX.XXX.147.http: R 106:106(0) ack 530 win 0 in slot1/tmm1 lis=NOS_Test
09:57:23.746419 IP XXX.XXX.XXX.144.51251 > XXX.XXX.XXX.16.http: R 106:106(0) ack 530 win 4909 out slot1/tmm1 lis=NOS_Test
BAD MEMBER
09:59:05.150720 IP XXX.XXX.XXX.99.51298 > XXX.XXX.XXX.147.http: S 261892195:261892195(0) win 8192 in slot1/tmm0 lis=
09:59:05.150744 IP XXX.XXX.XXX.147.http > XXX.XXX.XXX.99.51298: S 225654915:225654915(0) ack 261892196 win 4380 out slot1/tmm0 lis=NOS_Test
09:59:05.151035 IP XXX.XXX.XXX.99.51298 > XXX.XXX.XXX.147.http: . ack 1 win 256 in slot1/tmm0 lis=NOS_Test
09:59:05.152322 IP XXX.XXX.XXX.99.51298 > XXX.XXX.XXX.147.http: P 1:106(105) ack 1 win 256 in slot1/tmm0 lis=NOS_Test
09:59:05.152362 arp who-has XXX.XXX.XXX.153 tell XXX.XXX.XXX.142 out slot1/tmm0 lis=
09:59:05.153029 IP XXX.XXX.XXX.144.51298 > XXX.XXX.XXX.153.http: S 2929947028:2929947028(0) win 4380 out slot1/tmm0 lis=NOS_Test
09:59:05.152940 arp reply XXX.XXX.XXX.153 is-at 00:50:56:84:27:44 in slot1/tmm1 lis=
09:59:05.251401 IP XXX.XXX.XXX.147.http > XXX.XXX.XXX.99.51298: . ack 106 win 4485 out slot1/tmm0 lis=NOS_Test
09:59:08.151357 IP XXX.XXX.XXX.144.51298 > XXX.XXX.XXX.153.http: S 2929947028:2929947028(0) win 4380 out slot1/tmm0 lis=NOS_Test
09:59:11.351549 IP XXX.XXX.XXX.144.51298 > XXX.XXX.XXX.153.http: S 2929947028:2929947028(0) win 4380 out slot1/tmm0 lis=NOS_Test
09:59:14.551543 IP XXX.XXX.XXX.144.51298 > XXX.XXX.XXX.153.http: S 2929947028:2929947028(0) win 4380 out slot1/tmm0 lis=NOS_Test
09:59:17.751434 IP XXX.XXX.XXX.144.28570 > XXX.XXX.XXX.153.http: S 1018696290:1018696290(0) win 4380 out slot1/tmm0 lis=NOS_Test
09:59:20.751355 IP XXX.XXX.XXX.144.28570 > XXX.XXX.XXX.153.http: S 1018696290:1018696290(0) win 4380 out slot1/tmm0 lis=NOS_Test
09:59:22.400040 IP XXX.XXX.XXX.144.ssh > XXX.XXX.XXX.99.50902: P 3398111607:3398111675(68) ack 157644937 win 80 out slot1/tmm0 lis=
09:59:22.400513 IP XXX.XXX.XXX.99.50902 > XXX.XXX.XXX.144.ssh: P 1:37(36) ack 68 win 252 in slot1/tmm0 lis=
09:59:22.400870 IP XXX.XXX.XXX.144.ssh > XXX.XXX.XXX.99.50902: . ack 37 win 80 out slot1/tmm0 lis=
09:59:23.951673 IP XXX.XXX.XXX.144.28570 > XXX.XXX.XXX.153.http: S 1018696290:1018696290(0) win 4380 out slot1/tmm0 lis=NOS_Test
09:59:27.151393 IP XXX.XXX.XXX.144.28570 > XXX.XXX.XXX.153.http: S 1018696290:1018696290(0) win 4380 out slot1/tmm0 lis=NOS_Test
09:59:30.351698 IP XXX.XXX.XXX.144.51298 > XXX.XXX.XXX.153.http: S 2956356628:2956356628(0) win 4380 out slot1/tmm0 lis=NOS_Test
09:59:33.351467 IP XXX.XXX.XXX.144.51298 > XXX.XXX.XXX.153.http: S 2956356628:2956356628(0) win 4380 out slot1/tmm0 lis=NOS_Test
09:59:36.551418 IP XXX.XXX.XXX.144.51298 > XXX.XXX.XXX.153.http: S 2956356628:2956356628(0) win 4380 out slot1/tmm0 lis=NOS_Test
09:59:39.751838 IP XXX.XXX.XXX.144.51298 > XXX.XXX.XXX.153.http: S 2956356628:2956356628(0) win 4380 out slot1/tmm0 lis=NOS_Test
09:59:42.951662 IP XXX.XXX.XXX.147.http > XXX.XXX.XXX.99.51298: R 1:1(0) ack 106 win 4485 out slot1/tmm0 lis=NOS_Test
09:59:43.992057 IP XXX.XXX.XXX.99.51319 > XXX.XXX.XXX.147.http: S 1826829106:1826829106(0) win 8192 in slot1/tmm1 lis=
09:59:43.992086 IP XXX.XXX.XXX.147.http > XXX.XXX.XXX.99.51319: S 2526585337:2526585337(0) ack 1826829107 win 4380 out slot1/tmm1 lis=NOS_Test
09:59:43.992258 IP XXX.XXX.XXX.99.51319 > XXX.XXX.XXX.147.http: . ack 1 win 256 in slot1/tmm1 lis=NOS_Test
09:59:43.995470 IP XXX.XXX.XXX.99.51319 > XXX.XXX.XXX.147.http: P 1:106(105) ack 1 win 256 in slot1/tmm1 lis=NOS_Test
09:59:43.995533 arp who-has XXX.XXX.XXX.153 tell XXX.XXX.XXX.142 out slot1/tmm1 lis=
09:59:43.996152 arp reply XXX.XXX.XXX.153 is-at 00:50:56:84:27:44 in slot1/tmm1 lis=
09:59:43.996169 IP XXX.XXX.XXX.144.51319 > XXX.XXX.XXX.153.http: S 3086797946:3086797946(0) win 4380 out slot1/tmm1 lis=NOS_Test
09:59:44.094894 IP XXX.XXX.XXX.147.http > XXX.XXX.XXX.99.51319: . ack 106 win 4485 out slot1/tmm1 lis=NOS_Test
09:59:44.097300 IP XXX.XXX.XXX.99.51319 > XXX.XXX.XXX.147.http: R 106:106(0) ack 1 win 0 in slot1/tmm1 lis=NOS_Test