Paint peeling on outside wall is indicative of condensation; solve the moisture, solve the problem. Walls that are poorly insulated or not entirely airtight on the exterior surface invite moisture. Condensation happens when cold air from the outside works its way through the wall and chills the interior wall. Outside wall paint peeling is the result.
Condensation on wall surfaces is not uncommon in older homes. The walls are usually not well insulated or develop gaps in the mortar and the siding alloy. These cracks offer plenty of places for cold air to blow through.
Generally the moisture evaporates off and leaves little damage. This type of problem is more common in a confined area, like a closet or bathroom. Here the air is trapped and gives mildew the moisture and time it needs to grow. The frequency and concentration of moisture in your bathroom keep the walls wet longer and encourage the mildew to grow.
Before I discuss a remedy, consider another possible source for the problem. The roof or gutter may be the issue here. Sometimes water leaks from a roof or a gutter and runs down the interior of the wall. Depending on the season, this errant water could be caused by winter ice dams or excessive leaves in the gutter. Either situation could force water behind the facia board. Perhaps you remember ice dams on the roof in past winters? These problems may be more evident when investigated from a ladder.
When there are no indications of roof or gutter leaks, I would conclude the moisture is a result of poor insulation. You should check the exterior surface for cracks and caulk them closed. Then consider insulating the walls. This can be done with blown-in insulation from the inside or the outside. If the walls require repair from the mildew, then patching one-inch holes from blown-in insulation aren’t that big a deal.
If you can’t cure the problem due to costs or time, you can reduce it by increasing ventilation. I’ve installed metal vents in a closet door to allow air circulation. An exhaust fan in the bathroom is always a good idea. Finally, when whatever you do is done, paint the walls with a mildew-proof paint. It works great for us time and time again.