Interesting problem, and you found the right fix and saved yourself some money. I do believe that its mainly a physical/mechanical connection between the two, and they sometimes get loose or break....Story from our stay in US, 2 phase 110v. Main oven worked using both phases to get 220v, but some rings, timers etc just used 110v from one phase or the other. Suddenly most odd symptoms; nothing except the timer worked properly, rings would sort of work if oven turned on, etc. Oven experts declared we (or the landlords) needed a $300 new control unit.
By luck I absently mindedly twiddled the breaker before that arrived, and everything worked. What had happened was the breaker had tripped. Double ganged breaker (not sure what type, 1980) for each phase so if one side went down it should pull the other and trip. Turned out that it went the wrong way, one phase of the ganged breaker had tripped, but instead of pulling down the visible switch and breaking the other phase, the switch on the second phase kept the visible handle the first phase in the on position as if unbroken so breaker just looked normal.
You may laugh at what I am about to write, but the US electrical system is also a single 220VAC system, that many do call 2 phase, but really inaccurately, as its only a single phase to each house!
Often, transformers are used for each individual house, hanging on a pole nearby.
The difference being that in the USA, the middle point of the single phase is connected to and called Neutral.
Not at one end of a single phase as done in the UK and most of Europe.
Therefore in the USA, Neutral to either end of the (same) phase measures at around 110VAC.
You can see in this diagram, that its a single 220VAC phase from a transformer. But for for devices that need a lot of power, you can also get 220VAC simply by going from the phase end to phase end, which is really the same single phase, but people still believe its two phases - very misleading!
I dislike the US system, with it's dangerous plugs, and up till fairly recently, seldom an RCD (GFI) in sight.
They have significantly more deaths from shock per capita than the UK system, if I remember correctly.
The UK system, is to my mind the best and safest of all, if installed correctly and with modern extras like RCDs in use, fuses in plugs, lighting and power on different fuses/breakers, phase always defined and being switched etc..
The European system, sits somewhere between the two....slightly better than the US and far worse than the UK system....
Here is a reasonable explanation:-
or here with some good diagrams:-
Your Home Electrical System Explained
Master electrician explains your home electrical system in easy terms and with diagrams, so that you might become able to solve many electrical problems yourself.
thecircuitdetective.com
Andy