to stick with it / stay on the line
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to stick with it
To keep working persistently on something or toward a goal and not give up. It is a colloquial, separable verb.
Wenn du eine neue Sprache lernst, ist es wichtig, jeden Tag dranzubleiben.
When you're learning a new language, it's important to stick with it every day.
'Dranbleiben' is a separable verb. The prefix 'dran' (short for 'daran') goes at the end of the main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Auch wenn es schwierig wird, bleibe ich dran.
Even if it gets difficult, I'll stick with it.
The verb 'dranbleiben' belongs to colloquial language. It sounds motivating and is often used in informal conversations or advice.
Komm, bleib dran, du schaffst das!
Come on, stick with it, you can do it!
When you want to say what you are sticking with, you use the preposition 'an' with the dative. The combination 'an etwas dranbleiben' (to stick with something) is very common.
Ich bleibe an diesem Projekt dran, bis es fertig ist.
I'll stick with this project until it's finished.
You can clearly recognize the meaning 'to wait on the phone' from the context. It is used almost only in phone conversations, often together with words like 'verbinden' (to connect), 'Leitung' (line), or 'Moment' (moment).
Einen Moment, bleiben Sie bitte dran, die Kollegin kommt gleich.
One moment, please stay on the line; my colleague will be with you shortly.
to wait / maintain
'warten' and 'dranbleiben' can overlap when someone does not hang up on the phone. In that case, 'dranbleiben' means roughly: to stay on the line and keep waiting. But 'warten' is more general and fits many situations, not just on the phone. 'dranbleiben' is colloquial and also has a second important meaning: to keep working on something and not give up. That is why the two can easily be confused. If it is only about the time until an event, 'warten' is more natural. If someone is supposed to stay on the phone or not give up on a task, 'dranbleiben' fits better.
Bleiben Sie bitte dran, ich verbinde Sie mit der Kollegin.
Please stay on the line; I'll connect you to my colleague.
Vor dem Krankenhaus wartet der Fahrer auf den Patienten.
The driver is waiting for the patient in front of the hospital.