T-series instances use a concept of "burstable" performance where the instances has a number of CPU credits; when busy these are used; when idle credits build up. If there are no credits then the performance of the instance returns to a (lower) baseline. What you might be seeing is that you're running out of CPU credits. You can monitor the CPU credits so that might be worthwhile checking.
If this is causing the latency you might consider other instance types that do not use CPU credits (which is every other instance type) or you can enable Unlimited mode - noting that both of these solutions will have extra costs; and if you're using Unlimited mode all the time it it's best to consider a non-burstable instance type.
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