Participatory Budgeting (PB) processes are usually designed to span several years, with referenda for new budget allocations taking place regularly. This paper presents a first formal framework for long-term PB, based on a sequence of budgeting problems as main input. We introduce a theory of fairness for this setting, focusing on three main concepts that apply to types (groups) of voters: (i) achieving equal welfare for all types, (ii) minimizing inequality of welfare (as measured by the Gini coefficient), and (iii) achieving equal welfare in the long run. We investigate under which conditions these criteria can be satisfied, and analyze the computational complexity of verifying whether they hold.