It may be that DLM is making minor adjustments to your connection.
This is particularly likely in the early days of your connection.
It is common for DLM to force reconnections in the night when it decides to apply changes.
For me they have usually been at 2:00am; I don't know how it chooses the exact times.
Moved (with trepidation) to BT Infinity 2 for upload speed. Happy BE user for several years.