From what I know, there isn't a way to get free hourglasses anymore (aside from trading with hearts), but there is a way to reduce the use of them as much a possible; especially for missing chats. Just turn off your phone's "automatic date & time and automatic time zone" then, afterwards just turn back the time on your phone to match the chat's time(s). I believe there's is a limit like 6-8 hours before it doesn't work (or something like that), but I'm not exact on how much time it would take.
Hopefully Cheritz takes the new suggestions made by the players and actually implements more way to get hourglasses for this winter's content update!!
[EDIT]: The method above will get you permanently banned now after update 1.4.2. However, there is a new little method where you can get 50 hourglasses per attempt! (If you really need hourglasses, just keep doing this until you get enough of it.) I don't know for iOS users, but for android users, it works. I don't know how long this will keep working for, but Cheritz might find it and fix it soon, so do it while you still can!
Method:
1) Save your current progress
2) Go to the settings and start over
3) Go to to prologue
4) Don't bother answer anything, just spam the heck out of the back button on your phone. Say OK to backing out. A "duelist error" notice will pop up. Just press OK and keeping redoing this for more hourglasses. It's not a one time thing.