Lot's of things could account for broken spokes, from weight and riding style, to poor hardware, to poor wheelbuilding.

Some people are very married to their theory, and will always blame a single cause. But IME I've seen gorillas (pro football players) who rode like ballerinas, and at least one ballerinas that was harder on wheels than any gorilla I've ever met.

All things being equal, a fixed gear wheel will be stronger than a derailleur bike wheel, because the flanges are farther apart (always helps), and there's less tension difference between the right and left sides. Also bike factory wheels tend to be shorter lived than hand built after market wheels because of differences in hardware (plain gauge spokes vs butted for example, less concern for uniform tension, failure to effectively stress relieve the spokes, and other minor things that separate a well built product from a mass produced product.

Without actually seeing your wheel, and knowing how you ride, I can't pinpoint any one actual cause (only a mechanically knowledgeable psychic can), but given how many spokes have broken, I'd say it's time to rebuild fresh.

The one part least likely to be a cause is the rim, and also the hub, so it's probably safe to reuse both if they check out in good shape. For a stronger stiffer wheel, you might go to a wider, deeper rim, but without knowing more, I can't say whether it's necessary.