Up until the 90’s most flat roofs were constructed using roofing felt which would either be torched on roofing felt or a pour and roll roofing felt tacked onto the roof. As most felt roofs are laid as a low cost option (using a lower grade felt) these methods can have a relatively short lifespan. However when using higher grade or premium felt, most of which will be built up using differing numbers of layers and types of felt, will often have a lifespan of 10 to 25 years.

Often the weakest point on these types of roofs are the joints or laps of the roof as over time water can get in through these parts, especially if the roof is prone to pooling water (this usually happens when there is not sufficient drainage on the roof). This can cause the boards below the roof to soak in water and expand, which will trap moisture causing the felt to start to separate from the boards, which in turn allows more water to get through. 
For this reason it is recommended the roof should be inspected for leaks like this regularly so any issues can be rectified before major problems occur. This should be checked at least once a year, if not more.

As with all roof types eventually the felt will start to deteriorate over time, and become much more brittle and more likely to crack, so eventually the felt (and possibly the boards below) will need to be replaced. This deterioration can be down to any number of factors such as sun, heat, UV exposure and just the weather in general.

If you notice any of the issues mentioned above on your flat felt roof, this probably means it is time to start considering getting it replaced or (at the very least) repaired, although repair should be considered a sort term solution.
Repairs can be anything from a layer of Cromapol Paint to more Roofing felt being torched on in patches, evidence of either of these methods would be a sign that the roof has already had problems so replacement should be considered.