A damp patch on the ceiling tells you water is getting in, but it may not tell you where. Water can travel beneath a flat-roof covering before appearing inside, so the area immediately above the stain is only part of the assessment.
The covering may be damaged or deteriorated, or the problem may involve an edge, an upstand or a junction with an adjoining wall. Roof penetrations and drainage details also need attention where they are relevant to the leak.
Restricted drainage or standing water can be worth investigating, but ponding alone does not establish that a roof needs replacing. The covering, falls, outlets and accessible materials beneath need to be considered together. An assessment is needed to establish what has failed on your roof.