Did you replace the coolant tank because the vehicle was losing coolant in the first place? If so, there’s a chance that even though the coolant tank is brand new, there could be a leak from somewhere else in the system (that’s allowing the system to lose pressure, as you’ve identified). Possibilities include the radiator itself or even a head gasket, not to mention any one of a number of plastic fittings that control the flow of coolant to the engine and the car’s heating system. But don’t rule out the simple stuff, either; even the humble radiator cap or loose hose-clamp can allow pressure to leak from a cooling system.

The problem with a lot of imported cars is that they tend to use lots of plastic components in their plumbing systems. As they age (and at 16 years old, your car is hardly in the first flush of youth) these fittings and couples become brittle and can begin to leak or even fall apart altogether. In colder climates, these plastic bits and pieces don’t present the same problems to the same degree, but here in Australia, our hot-climate heat-cycles are not appreciated by some makes and models. Combine that with a modern, pressurised cooling system, and you have yourself a problem.

I doubt the E39 will ever be considered a classic, particularly a run-of-the-mill model like the 525i. If I were to buy one I would buy the six-cylinder.

The best option for you is probably to ditch the run-flats and fit regular radials. You can then run a regular spare and you could buy a jack from your local auto accessory store.