Thanks for taking the time to look at my problem. The trunks are ISDN-PRI. I've posted 2 traces below. We occassionally see denial event 1240, but by the time the denial event shows up in the trace, the call is connected.
(1240 No response to IGAR DTMF E-sigged digits three times with no response from the far end.)
x24008(NR1) calling x80147(NR8) -- 6 second delay on answer
IGAR LDN in NR8: 3045283190
12:02:40 active station 24008 cid 0x1836
12:02:40 G711MU ss

ff ps:20 rn:1/1 10.165.86.83:28008 10.185.41.20:62420
12:02:40 xoip: fax

T modem

ff tty:US 10.185.41.20:62420 uid:0x7a4f
12:02:41 dial 80147
12:02:41 ring station 80147 cid 0x1836
12:02:41 IGAR starting call app A station 80147 cid 0x1836
12:02:41 G711MU ss

ff ps:20 rn:8/8 10.186.74.233:3218 10.186.41.43:2692
12:02:41 xoip: fax

T modem

ff tty:US 10.186.41.43:2692 uid:0x7f28
12:02:41 dial 13045283190# route

REFIX|FNPA|ARS
12:02:41 term trunk-group 4 cid 0x183d
12:02:41 dial 13045283190# route

REFIX|FNPA|ARS
12:02:41 route-pattern 90 preference 1 cid 0x183d
12:02:41 seize trunk-group 4 member 187 cid 0x183d
12:02:41 Calling Number & Name 3037125190 NO-CPName
12:02:41 Proceed trunk-group 4 member 187 cid 0x183d
12:02:41 tone-receiver 01AXX02 cid 0x183d
12:02:43 Alert trunk-group 4 member 187 cid 0x183d
12:02:43 active trunk-group 4 member 187 cid 0x183d
12:02:47 IGAR active call app A trunks 4/187 & 80/47 cids 0x183d & 0x1841
12:02:47 idle cid 0x183d
12:02:47 G711MU ss

ff ps:20 rn:1/1 10.165.86.83:28008 10.185.41.10:23300
12:02:47 xoip: fax

T modem

ff tty:US 10.185.41.10:23300 uid:0x7a4f
12:02:49 active station 80147 cid 0x1836
12:02:49 G711MU ss

ff ps:20 rn:8/8 10.186.74.233:3218 10.186.41.43:2716
12:02:49 xoip: fax

T modem

ff tty:US 10.186.41.43:2716 uid:0x7f28
12:02:49 dial 13045283190# route

REFIX|FNPA|ARS
12:02:49 term trunk-group 4 cid 0x1855
12:02:49 dial 13045283190# route

REFIX|FNPA|ARS
12:02:49 route-pattern 90 preference 1 cid 0x1855
12:02:49 seize trunk-group 4 member 187 cid 0x1855
12:02:49 Calling Number & Name 3037125190 NO-CPName
12:02:49 Proceed trunk-group 4 member 187 cid 0x1855
12:02:49 tone-receiver 01B0103 cid 0x1855
12:02:51 Alert trunk-group 4 member 187 cid 0x1855
12:02:51 active trunk-group 4 member 187 cid 0x1855
12:02:52 denial event 1240: No response to IGAR DTMF D1=0xc8 D2=0x1481e2
12:03:32 idle station 24008 cid 0x1836
12:03:32 idle cid 0x1855
12:03:52 TRACE COMPLETE station 24008 cid 0x1855
x24008 calling x80147 Delay of 6 seconds before hearing call. MOH immediate
IGAR LDN for NR1: 3037125190
11:50:54 active station 24008 cid 0x12c8
11:50:54 G711MU ss

ff ps:20 rn:1/1 10.165.86.83:28008 10.185.41.22:38476
11:50:54 xoip: fax

T modem

ff tty:US 10.185.41.22:38476 uid:0x7a4f
11:50:56 dial 80147
11:50:56 ring station 80147 cid 0x12c8
11:50:56 IGAR starting call app A station 80147 cid 0x12c8
11:50:56 G711MU ss

ff ps:20 rn:8/8 10.186.74.233:3218 10.186.41.38:3224
11:50:56 xoip: fax

T modem

ff tty:US 10.186.41.38:3224 uid:0x7f28
11:50:56 dial 13045283190# route

REFIX|FNPA|ARS
11:50:56 term trunk-group 4 cid 0x12c9
11:50:56 dial 13045283190# route

REFIX|FNPA|ARS
11:50:56 route-pattern 90 preference 1 cid 0x12c9
11:50:56 seize trunk-group 4 member 187 cid 0x12c9
11:50:56 Calling Number & Name 3037125190 NO-CPName
11:50:56 Proceed trunk-group 4 member 187 cid 0x12c9
11:50:56 tone-receiver 01AXX05 cid 0x12c9
11:50:58 Alert trunk-group 4 member 187 cid 0x12c9
11:50:58 active trunk-group 4 member 187 cid 0x12c9
11:51:01 IGAR active call app A trunks 4/187 & 80/47 cids 0x12c9 & 0x12d0
11:51:01 idle cid 0x12c9
11:51:01 G711MU ss

ff ps:20 rn:1/1 10.165.86.83:28008 10.185.41.10:22568
11:51:01 xoip: fax

T modem

ff tty:US 10.185.41.10:22568 uid:0x7a4f
11:51:04 active station 80147 cid 0x12c8
11:51:04 G711MU ss

ff ps:20 rn:8/8 10.186.74.233:3218 10.186.41.38:3228
11:51:04 xoip: fax

T modem

ff tty:US 10.186.41.38:3228 uid:0x7f28
11:51:04 dial 13045283190# route

REFIX|FNPA|ARS
11:51:04 term trunk-group 4 cid 0x12dc
11:51:04 dial 13045283190# route

REFIX|FNPA|ARS
11:51:04 route-pattern 90 preference 1 cid 0x12dc
11:51:04 seize trunk-group 4 member 187 cid 0x12dc
11:51:04 Calling Number & Name 3037125190 NO-CPName
11:51:04 Proceed trunk-group 4 member 187 cid 0x12dc
11:51:04 tone-receiver 01B0108 cid 0x12dc
11:51:06 Alert trunk-group 4 member 187 cid 0x12dc
11:51:06 denial event 1240: No response to IGAR DTMF D1=0xc8 D2=0x1481c0
11:51:06 active trunk-group 4 member 187 cid 0x12dc
11:51:44 hold station 24008 cid 0x12c8
11:51:55 unhold station 24008 cid 0x12c8
11:51:55 G711MU ss

ff ps:20 rn:1/1 10.165.86.83:28008 10.185.41.10:22568
11:51:55 xoip: fax

T modem

ff tty:US 10.185.41.10:22568 uid:0x7a4f
VOIP data from: 10.186.41.45:2812
11:52:05 Jitter:0 0 0 0 0 0 0 0 0 0: Buff:8 WC:5 Avg:0
11:52:05 Pkloss:0 0 0 0 0 0 0 0 0 0: Oofo:0 WC:0 Avg:0
VOIP data from: 10.185.41.10:22568
11:52:07 Jitter:0 0 0 0 0 0 0 0 0 0: Buff:11 WC:1 Avg:0
11:52:07 Pkloss:0 0 0 0 0 0 0 0 0 0: Oofo:0 WC:0 Avg:0
VOIP data from: 10.186.41.45:2812
11:52:15 Jitter:0 0 0 0 0 0 0 0 0 0: Buff:8 WC:5 Avg:0
11:52:15 Pkloss:0 0 0 0 0 0 0 0 0 0: Oofo:0 WC:0 Avg:0
VOIP data from: 10.185.41.10:22568
11:52:15 Jitter:0 0 0 0 0 0 0 0 0 0: Buff:11 WC:1 Avg:0
11:52:15 Pkloss:0 0 0 0 0 0 0 0 0 0: Oofo:0 WC:0 Avg:0
11:52:23 idle station 24008 cid 0x12c8
11:52:23 idle cid 0x12dc
11:52:25 TRACE COMPLETE station 24008 cid 0x12dc