you have bgp peer on gig interface, which should not be genrally causing any bottleneck,
to troubleshoot this further i would perform following task to further isolate the issue.
1. check if the CPU is highly ustilised when the telco reports any missing keepalive, when cpu is high i may missout to process the control packets even if its high priority
2. control plane traffic is by default prioritized over the data traffic either by pak_priority or ip precedence
3. also it will be great to have wireshark capture on this gig interface which will prove the point that if bgp keepalive are sent out, this will be thw proving point
hope this helps