How do I get dough to stiffen up so cut out cookies won't lose their shape when transferred onto sheet?

I am making cookie ornaments for our church children to decorate and my first batch turned out great but the second batch is very sticky and won't keep their shape after I use the cookie cutters. I have added more flour but that didn't help at all. The problem happens when I try to get the shapes out of the dough and transfer it to the cookie sheet. They stretch out and look like something that you would see in a funhouse mirror! Any suggestions of how to salvage my dough?