Calls making short 'blip' and disconnecting

Question

Hello everyone,
I'm having a strange issue and was wondering where I should start my troubleshooting. (We're using CallManager Express)
My receptionist tells me that during the week, randomly and intermittently, when someone calls the main phone line, the phone makes a short 'blip' sound and shows up as a missed call.
The night service setting was a suspicion but that's configured correctly everyday from 5pm to 8am the next day.
Has anyone seen this happen and could help me?
Thanks,
Ali

Answer 1

Very informative, thanks Fred.
The
network-clock-participate wic 1
was already configured on the router, but I added
network-clock-select 1 t1 0/1/0
and it set the line as primary clock source. Before that it was
sh network-clocks
Network Clock Configuration
Priority Clock Source Clock State Clock Type
10 Backplane GOOD PLL
Current Primary Clock Source
Priority Clock Source Clock State Clock Type
10 Backplane GOOD PLL
and now it's
sh network-clocks
Network Clock Configuration
Priority Clock Source Clock State Clock Type
1 T1 0/1/0 GOOD T1
10 Backplane GOOD PLL
Current Primary Clock Source
Priority Clock Source Clock State Clock Type
1 T1 0/1/0 GOOD T1
I tried adding network-clock-participate aim as well but it said the slot doesn't support or is empty so forget that...
Do you think this would alleviate the problem?
Here's a partial config of the router:
memory-size iomem 10
clock timezone PST -8
clock summer-time MST recurring 2 Sun Mar 2:00 1 Sun Nov 2:00
network-clock-participate wic 1
network-clock-select 1 T1 0/1/0
no ip source-route
ip tcp synwait-time 10
voice-card 0
no dspfarm
voice service voip
allow-connections h323 to h323
allow-connections h323 to sip
allow-connections sip to h323
allow-connections sip to sip
supplementary-service h450.12
h323
sip
registrar server expires max 3600 min 3600
voice class codec 1
codec preference 1 g711ulaw
voice translation-rule 1
rule 1 /6779/ /5001/
rule 2 /6779/ /2001/
rule 3 /0419/ /2098/
rule 4 /0418/ /7777/
voice translation-rule 2
voice translation-rule 9
rule 1 /^911$/ /911/
rule 2 /^9\(.*\)/ /\1/
voice translation-profile IncomingMain
translate called 1
controller T1 0/1/0
mode ccs frame-forwarding
framing esf
linecode b8zs
channel-group 1 timeslots 13-24
ds0-group 0 timeslots 1-10 type e&m-wink-start dtmf dnis
translation-rule 1
Rule 1 6779 5001
Rule 2 6775 2099
Rule 3 #### 2001
Rule 4 0418 7777
Rule 5 0417 2010
voice-port 0/0/0
voice-port 0/0/1
voice-port 0/1/0:0
translate calling 1
translate called 1
voice-port 0/3/0
auto-cut-through
operation 4-wire
signal immediate
voice-port 0/3/1
operation 4-wire
Thanks again,
Ali