To me, it looks like it could be the brick stitch, as shown in this tutorial http://crochet.about...y/blcrazyst.htm
but with 3 stitches per "brick" rather than 4.
Due to the years of use, the stitches have stretched in places and compacted in others, so i think that any new piece of crochet is not going to really look exactly like it, even if it is the same stitch pattern.
Following what Jennifer said in post 2, you could try doing 2hdctog, chain 1, then on the next row do the 2hdctog into the chain space, that might look very similar.
It's very cool that you still have and use it!
Oh, and welcome to the ville