Is it normal for a fixed gear bicycle's rear wheel to slip forward in its dropouts from time to time?
This can be a fairly common occurrence with a fixed wheel bike. It may depend on a few different things, ie what sort of nuts you are using, how tight they are, what style of dropouts, and what the dropouts are made of.
A different sort of nuts may help. eg something with serrated nuts or washers could grip better. Also you may be able to tighten the nuts more, maybe a bit higher than what Park recommend.
Probably the best option is to use chaintugs. These fit on the dropouts, and have some sort of screw to hold them in place. So this stops the axle from moving forward. Usually you only need one, on the drive-side dropout, though you can use one on each side if you want.
One example is the Surly Tuggnut.

(source: surlybikes.com)