A number of things can be causing this issue. Let's eliminate these one-by one:
1. NO SEEDERS: The most common issue is the torrent does not have enough people sharing the file or "seeders". You can check to see if there are enough seeders for the file by checking the file using this website - https://checker.openwebtorrent.com/
2. WIFI ONLY MODE: Your app is in ‘wifi-only mode’ and you are not on a wifi network. To check this, tap on the menu button (three dots) in upper corner of the screen in portrait (vertical) mode, then tap on ‘Settings’. Turn off the switch for ‘Use Wi-Fi networks only’, then toggle it once to make sure it is off. This will turn it red.
3. POOR CONNECTION: Your network connection is poor (common). To check this, try streaming content on your browser or an app (e.g YouTube). If you can stream content without too much buffering, then you probably have a strong connection. Alternatively, check your wifi speed with the free Speed Test app from Google Play. Here's a popular one - https://play.google.com/store/apps/details?id=org.zwanoo.android.speedtest
4. BLOCKED WIFI: Your wifi network connection is blocked by the ISP. This means your network is blocking torrent files, or is blocking your outgoing port. To check this, try downloading a Featured Content torrent on another network. If you can download a torrent on another network (particularly a fast wifi network), then it’s likely that your wifi network is causing the issue. To fix this, tap on Menu, then Settings, then Incoming TCP Port in our app. Look at the TCP Port number, and increment it up by one. For example, if your port number is 6881, make it 6882. If this doesn’t work, your wifi network may be throttling BitTorrent traffic, in which case we can't help with a workaround.
5. PHONE ISSUE: The app isn't working well with your device. To check this, delete any unfinished torrents, then close the app. Next, delete BitTorrent app data by going to your phone’s Settings, then App, then BitTorrent, then Storage, then Clear Data. Next, reboot your phone, then uninstall and reinstall the app, then reboot your phone again. Then try downloading a test torrent here - https://webtorrent.io/free-torrents
6. NOT SHARING FILES: You are not seeding, and the swarm is ignoring you. If you are not seeding, you may be anonymously identified by the swarm as a leecher. Leeching means you download, but you don’t share. Some users reporting slowdowns after using the app for a long time are having this issue due to not seeding. To check this, go to your phone’s Menu, then Settings, then Upload limit, then change this to a reasonably number (not zero). Try seeding a little, and see if your torrents start speeding up. But please don’t do this with your data plan. Use wifi-only mode, which is also under Settings.