Stop paying people to fix simple problems and then the repair/replace question falls back over to the repair side easily. You'll also know upfront how much the repair is likely to cost since you'll have a good idea of what parts you need and for how much prior to making any financial commitment. Not only do you stop paying $100/hr+tax for labor, but you get your parts cheaper by sourcing them from discount parts stores. You don't have to wait around at home for a repairman, and you learn something in the process too.
My general rule of thumb is when parts start to hit 50% of cost, energy efficiency is significantly better with a new unit, or I foresee the breakdown rate increasing too high therefore taking too much of my time.
Last year my HVAC motor died. $200 later and I was back up and running in one morning. Had I called an HVAC specialist he would have driven out to my house, checked to see what parts he needed, had to go back out to get them, and then came back to install them. I would have been sitting home doing nothing except paying someone else to do all that stuff for me. I had no prior HVAC experience other than cleaning the air filter, but I do know how to turn a wrench.
Just yesterday, I changed the front brakes on my Forester in under 2 hours, and it cost me $40 (could have cost me $25, but I bought the "fancier" brake pads in hopes that I don't have to replace them as often. Oh, and I'll never have to pay for brake pads again on my Forester as they have a lifetime warranty.
Also, don't waste your money on "luxury" brands like Bosch. Bosch dishwashers advertise the lack of a hard food disposer and then have the nerve to charge you more for taking away a feature compared to the competition. Compared to an equivalent Maytag with hard food disposer and is cheaper (and plenty quite, I can't hear mine operating).