I'd faced a similar problem a few months back where the agent wasn't able to process the large log file after a massive update in the 300 sec timeout window and was failing as a result. This issue was addressed by extending the timeout (to 1200 sec in my case).

Distributor and Log Reader Agent profile property: Query Timeout.

Here is the error profile to compare:

Error Message:

The process could not execute 'sp_repldone/sp_replcounters' on 'DB'.

Timeout expired

(Source: ODBC SQL Server Driver (ODBC); Error number: 0)

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The process could not set the last distributed transaction.

(Source: DB (Agent); Error number: 22017)

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