This is by design. DMV data is dropped when SQL Server is restarted. If you want to keep them you need to do some data collection into permanent tables either locally or on a central management server.

What other issues do you think are linked ?

The SQL engine does not use the data in these DMV's for anything so the lack of data in the DMV's is not likely to cause other issues. When SQL Server is restarted the plan cache is cleared so on restart you may see new plans being generated. The plan that is generated is often optimized for the @parameters passed the first time the procedure is called so this can lead to unexpected plans in cache that may not be optimal for other workloads.