Yes, storage carries forward between Acts. Items you stored in Act I will be available in Acts II and III, etc.
Watch it with off-path storage in Act II. Use only the on-path storage (in Vergen, on Iorveth's path; outside the camp, on Roche's path). Using the other path's storage will cause lost items.
Thanks, Guynwah. I had read your response to this topic a few days ago and had to search to find it again. Your detailed answer helps to enjoy the game instead of searching forever looking for storage spots, which is how I found the one it Act I.