Commuting successfully, and with the same ease and reliability as driving, requires:

1) a well-maintained quality bike,
2) equipped for how you ride and what you need to carry, and
3) some experience as a rider.

It sounds like you have either a poorly maintained, or a crappy bike, and you need some experience. You can buy the first two, but the third comes only with time.

I started out after not having been on a bicycle in 35 years. To offset my inexperience with bikes and maintenance, I bought a brand new LBS bike, but almost the cheapest model they had ($380, about $450 these days.)

The decent quality bike (albeit a cheap one, that was heavy as an anvil) let me focus on becoming experienced. I made tons of mistakes as a rider along the way It was also four to five months before my body was back in shape and things were flowing smoothly. I haven't missed a day since things finally got sorted out. As of the end of last week, I have 1,533 consecutive workdays of bike commuting. Given my four-day workweek, you can easily figure out that's just over seven years.

It did not go smoothly at first. The bike went on the bus a few times. And I crashed and fell off four times in the first couple of years. My first flat made me feel like a complete idiot. Maintenance I learned slowly with the help of the mechanics at my LBS, who, knowing I was using the bike as a commuter, cut the repair queue for me when I came in with questions and repairs.

Other than the odd flat tire, I haven't had to do any in-ride repairs in years. That's because I've learned how to spot trouble ahead of time, and how to maintain my bikes before trouble happens. (It helps that I also buy quality stuff.) I haven't crashed since that Pontiac hit me five years ago. Simply because variety is the spice, these days I have two bikes completely outfitted for commuting, (rear racks, full fenders, puncture-resistant tires, on-board toolkit and pump, dynamo lighting systems, backup battery lights too). But one bike can also back-up the other.

All this took time. Given time, you can turn around your record too.