You don't say the airline(s) involved, but this is actually fairly normal so I would not worry about it.
If your 2nd flight is on a smaller "regional" carrier they may not be set up to do on-line seat assignments, where everyone gets their assignment at the gate. It is becoming rare that this is the case but it still happens. Another case is when they need to swap out aircraft type and because of the different configuration need to reassign several people.
Most major airlines will "open" the flight about 60 minutes before the flight, if you are on a smaller carrier they may not be there until 45 minutes before. I would plan to get to the gate closer to the 60 minutes, as the worst thing is you will be there a few minutes waiting for them to arrive.
If this is just a case where all of the open seats were taken, you will still get a seat. But like your first flight they may not be together.
You could also try at your original departure airport to go to the check-in counter pre-security and see if they can assign you seats at that point. Again sometimes they can, sometimes they can't. This is the same place you will drop off your checked bags.
As another tip I would suggest looking at the flight information board as soon as you arrive off of your first flight. Find the gate for your next flight and be in that area so you have an idea of where it is. After that you do not need to be back at the gate until as I mentioned about an hour before your flight so you are free to go get something to eat or walk around.