Amir,
Solr is stable. If you are not convinced, have a look at list of users here... http://wiki.apache.org/solr/PublicServers which include NASA, AT&T etc...
Solr main goal is to serve as Search engine, helping us to implement search, NLP algorithms, Big Data issues, etc. Solr is not meant to be main data store (also it might serve as one....
Reason for the ambiguous sentence above is that unlike relational database, Solr can store both original data and index OR the INDEX ONLY without the data itself.
If you store only the index, by specifying in Solr schema.xml Stored="false" per field, then you get a much smaller Solr data volume and better performance, but when you query Solr you will receive back only the document ID, and you will have to continue with your relational DB.... Of course you can store some of the data, some of document field, and avoid storing some.
Of course, you should backup/ replicate Solr to ensure disaster recovery, etc.