I was going to get my CDL while I was still working at my current employer,that way if something ever happens I would have my CDL in my pocket and could go driving a truck.
But I hear a lot of companies want you to retrain if there's one month gone by without driving a truck,is this true?

Yes, it is basically true.

For every 30 days that pass between graduating CDL school and starting your first trucking job fewer companies are willing to hire you unless you go through school again. By the time you hit 6 months the pickings are quite slim, and after a year it usually comes down to praying someone will give you a job.

Granted, there are companies that only care if you have a CDL and/or that you went to school. For the most part these companies do not show up on anyone's first, second or third choice lists.