Duolingo has a great feature when it comes to offline practicing, but unfortunately the points accrued do not apply to the streak counter. I was in the mountains this past Friday and practiced offline, but this activity did not register on Duolingo. I can only assume this was due to the fact that my phone's data was turned off for the entire day. Luckily, I had a streak freeze implemented for such a situation, but hopefully this is a bug which might be addressed in the near future.
Thanks for reading!
Today, it looks like the app, while offline, keeps track of your streak. Then when you get back online, it synchs with the server and the timestamps of your training doesn't accrue. Maybe it all goes in to the first day or some of it also seems to get lost since some training that I know I did is gone.
Anyway, offline streaks can only seem to be maintained for 24 hours. Then they are lost. So try and log on and do one training once per day and it works. Otherwise, your streak is gone, or you need to buy a lot of streak repairs.