What does "Let me know if the problem persists" exactly mean? [duplicate]

Solution 1:

Ambiguous.

In informal writing, "if" and "whether" are used interchangeably.¹ This is not recommended because it creates ambiguity, but it is an unfortunate fact. Consequently, the statement can mean either:

Let me know whether the problem persists.

or:

Let me know (only) if the problem persists.

Solution 2:

A logician might say that the person being addressed need say anything only if the problem did persist. In practice, the context will usually make it clear what is required.