I can't speak for frozen fish food specifically, but if we assume that it's the same as other food; yes - but the "when" is the hard part.
Food in a freezer is impacted by a couple of factors that can shorten it's viable usability.
The first (and most common problem) is dehydration - aka "freezer burn". Freezer burn doesn't make the food "unsafe", just less palatable. I have no idea to what degree fish "taste" their food (do fish have tongues?!? How do I not know that?!?) or, if they do, how finicky they are to the off flavors that come from this state. Note that properly sealed containers can dramatically reduce the potential for dehydration (the small, sealed Hikari packaging, for example, are great for this reason alone).
Another common problem is flavor (aroma) transference. Given enough time, improperly sealed food will "bleed out" it's aromas into the freezer. Other foods can then absorb those aromas. This can make for some rather off tastes. Again; not sure how this impacts fish food... (Side note: this is actually a food preparation method that is not all that uncommon. For example; storing truffles in rice keeps the truffle dry (good for the truffle) and also flavors the rice with truffle - win/win.)
Finally (though there are other factors, I'm trying to stick to the big ones), food can be damaged during storage due to crystalline formation. This results when the water inside the food melts (unlike freezer burn - which is sublimation (solid water to gas water directly), this is solid water to liquid water I'm talking about), it will them refreeze in the form of ice crystals. This process will occur in conventional freezers during the defrost cycle. These cycles allow the temperature in the freezer to raise slightly (melting the ice that's formed on the sides/shelves of the freezer is the goal) before chilling it back down. The defrost cycle is "nice" for what it's intended to do, but for sensitive foods (such as fish food that has a low volume, and is thus easily impacted by temp swings), the defrost cycle can result in an accelerated breakdown in the food. As ice crystals form inside of the food, they can shred the structure of the food. Much like freezer burn, this may not impact the safety of the food, but will impact it's texture.
So, in short; I guess it depends upon how much fish care about the flavor and texture of their food (which I don't know, myself). I've heard that some fish can be picky eaters, so this may indicate that the quality of the food does actually matter. Which would mean that frozen fish foods do, in fact, have a shelf life. Determining just what this is will be very hard, however, as there are numerous variables involved. Two of the key ones is how often you open your freezer and how long you leave it open for. Opening infrequently and closing quickly can increase the shelf life of all your foods significantly.
It's not just about taste, but also about rancidity/oxidation. Not only does it add harmful products to the food, it removes vitamins/nutritional value. The longer it is frozen, the more free radicals it will contain and the less nutritional value it will have.