Network bandwidth burst exhaustion

A latency-sensitive API on a cloud VM instance type develops slow, creeping degradation: it runs perfectly after any restart, then over ~30-60 minutes p99 and packet-level latency climb and connection timeouts appear, and a restart (or moving to a fresh instance) resets it. The degradation correlates with sustained outbound throughput from a colocated batch job that ships large datasets out of the same instance. CPU, memory, and disk are all fine throughout. The instance type advertises a 'baseline' network bandwidth with a burstable allowance. How do you triage and what's happening?