The preposition depuis with the imperfect indicates how long something had been going on in relation to a past event.
Basic sentence meaning and construction are similar to those of depuis with present. Depuis with imperfect may indicate either duration or a temporal starting point.
what had been going on ...
past event
translation
Tammy attendait Tex depuis une heure ...
... quand il est entré.
Tammy had been waiting for Tex for an hour ... when he came in.
Tammy souhaitait avoir une discussion sérieuse depuis lundi ...
... quand enfin le moment s'est présenté.
Tammy had been wanting to have a serious discussion since Monday ... when at last the opportunity presented itself.
Duration may also be indicated with il y avait ... que,
cela faisait ... que and, more emphatic, voilà que.
The first sentence above could also be expressed as:
Il y avait ... Cela faisait ... Voilà ...
une heure que Tammy attendait Tex.
Tammy had been waiting for Tex for an hour.
Listen to the dialogue:
Tammy: Salut, Tex. Ça va?
Tammy: Hi Tex. How are you?
Tex: Non! Hier, j'étais à la bibliothèque depuis deux minutes quand l'alarme à incendie a sonné. Je n'ai pas pu travailler! Ensuite à la caféteria, je faisais la queue depuis une demi- heure, lorsqu'ils ont annoncé qu'il n'y avait plus de sandwiches! Je suis allé faire cours sans avoir mangé!
Tex: Not well! Yesterday, I had been in the library for two minutes when the fire alarm went off. I was not able to work! Then at the cafeteria, I had been waiting in line for half an hour when they announced they had run out of sandwiches! I went to teach without eating!
Tammy: Pour moi non plus, rien ne va comme je veux! Depuis lundi je voulais te parler, mais ce matin tu as dit que tu avais trop de travail!
Tammy: Nothing is going the way I want either! I had been wanting to talk to you since Monday, but this morning you said you had too much work!
Duration may also be indicated with 
