I agree with Mauricio Scheffer solution.
If that can help, I transformed my initial query:
DocSource:"P" OR ( DocSource:"E" AND (MyDate:[NOW TO *] OR -MyDate:[* TO *] ) )
To
DocSource:"P" OR ( DocSource:"E" AND -( -MyDate:[* TO NOW] AND MyDate:[* TO *] ) )
The first query didn't run as expected in Solr 4.1.