I bought and planted a young Guava tree, about a foot high, which is supposed to withstand frosts down to 5 degrees Celsius. The leaves are going brown and falling. Some leaves are brown down one side but green on the other.

Given the weather over the last week, you may have already found the answer to your question. Guavas thrive in places like Fiji and barely grow in the top of the North.

So it sounds to me like your plant may well be suffering from frost burn. Covering it with a frost cloth, available from garden centres, could help it survive the winter. If you haven’t had a frost yet, the cause may be an insect like thrips. The best way to beat them is with neem oil.