How do I keep my fish from dying?

For a whopping 25,000 credits, the Aquarium VI is available for sale on the Citadel, at the Elkoss Combine Arsenal Supplies terminal (where you first find Barla Von) in the Presdium Commons.

In addition to breaking your piggy bank, this pricey item's description also indicates that it will automatically feed your fish:

With so many exotic speices of fish available in today's galactic market, it takes an expert to maintain an ideal aquarium. This VI automatically dispenses food, adjusts the temperature, pH, and algae content of the water, and even talks to the fish when you're not around, leaving you free to enjoy your aquatic friends without fear of killing them.

If 25,000 credits isn't expensive enough for your tastes, you can also head on down to the Alliance Requisitions terminal in the Normandy's cargo bay, where you can buy the same Elkoss Combine Aquarium VI for base price + a 2,500 credit markup.

As I recall from ME2, if you didn't go and feed your fish after every mission (though some have said they've done up to three missions before expiration) they'd die. I would imagine it is the same for ME3. I ponied up the cash for the VI because by golly I hate seeing dead fish and feeling like a total failure as a human being as a result.