
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.
permanent / lasting
Both words describe a state that continues for a long time. “Anhaltend” primarily emphasizes uninterrupted continuation without claiming that the state will last permanently. “Dauerhaft” is appropriate when a state is meant to remain in place over the long term; “anhaltend” is appropriate when you want to emphasize that it is still continuing.

Die anhaltenden Bauarbeiten sorgen weiterhin für weniger Verkehr.
The ongoing construction work continues to reduce traffic.
Die neue Regel soll dauerhaft für weniger Verkehr sorgen.
The new rule is intended to permanently reduce traffic.