The work done when mining is not accumulated over time. Each hash calculated is independent from the others. Think of mining as repeatedly rolling a huge die and trying to get an extremely low number, instead of working towards a solution of a complex problem.

If a miner loses connection to the internet, it will be unable to submit work during this time period. Work done during the outage may or may not be stale (too old to submit) when connectivity returns. However, no previous work will be lost, as this work would have already been submitted immediately to a pool/the bitcoin network if it was useful.