Playing Houkago Girls Tribe（放課後ガールズトライブ）has been a pain in the ass. Let me explain the situation a little bit.
1. Using a Japanese IP
The game only allows Japanese IPs to access it. We all who live outside Japan MUST download a VPN app and select a Japanese server in order to launch the game successfully. HOWEVER, using a VPN may slow down our internet connections as the server we are connected to could be unstable.
From my experience, some VPN apps provide better connections. So, be sure to try different apps and see which works best for you.
— 【公式】放課後ガールズトライブ/ガルトラ (@garu_tora) December 23, 2016
The game was under urgent maintenance from 22nd December to 23rd December. Therefore, it seems like the game server itself is not as reliable as we thought it would be. If you have troubles entering the game and you are sure the internet works completely fine, it is very possible that it is under maintenance. Whenever there is an urgent maintenance, the game’s official twitter posts a tweet titled "緊急メンテナンスのお知らせ". In short, check out the official twitter if you have troubles accessing the game server while you are fine playing other games using a VPN.
3. Connection timeout（タイムアウト）
Receiving a "タイムアウト" message is much less scary then reading a post about maintenance. Connection timeout can be fixed in two ways.
First, simply close the app and launch it again.
Second, if the method mentioned above fails, tap "キャッシュクリア" on the title screen to clear cache.
There is also another "キャッシュクリア" button on the in-game menu. Tap "menu" → "その他", and you will be able to find the said button there. Remember to tap the orange "yes" button to proceed. After the above procedure is done, close the app and launch it again.
Wish you guys a Merry Christmas and a Merry Gaming Christmas.