anhaltend
persistent
Continuing over a longer period of time without interruption; unceasing.
Der anhaltende Regen führte zu Überschwemmungen.
The persistent rain led to flooding.

persistent
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persistent
Continuing over a longer period of time without interruption; unceasing.
Der anhaltende Regen führte zu Überschwemmungen.
The persistent rain led to flooding.

'Anhaltend' (persistent) is the present participle of the verb 'anhalten'. The verb 'anhalten' can mean 'to stop', but also 'to continue/last'. The adjective 'anhaltend' (persistent) is derived from the second meaning and describes something that continues.
Die Polizei warnt vor der anhaltenden Glätte auf den Straßen.
The police are warning of the persistent ice on the roads.
'Anhaltend' (persistent) usually describes processes or states. Common combinations are 'anhaltender Regen' (persistent rain), 'anhaltende Probleme' (persistent problems), 'anhaltender Erfolg' (lasting success), or 'anhaltender Applaus' (sustained applause).
Trotz anhaltender Kritik hält der Politiker an seinem Plan fest.
Despite persistent criticism, the politician is sticking to his plan.
You can also use 'anhaltend' (persistently) as an adverb to describe how an action happens: namely, without interruption. In this function, it is not declined.
Die Fans applaudierten anhaltend.
The fans applauded persistently.
constant
'ständig' and 'anhaltend' can both mean that something does not stop quickly. The difference is in how they view duration. 'ständig' often says that something happens very frequently or keeps repeating. In everyday language, it often sounds a bit annoyed. 'anhaltend' is more about a state continuing for a long time without interruption, for example rain, pain, or noise. They can be confused because both express duration. If something happens again and again, 'ständig' fits better. If something continues without stopping, 'anhaltend' is more precise.

Wegen des anhaltenden Regens fällt das Training heute aus.
Because of the persistent rain, training is canceled today.
Ihr vergesst beim Einkaufen ständig die Milch.
You constantly forget the milk when shopping.