It's important to save your fleets when you're not OnLine. Reason as long as your fleet is still on your home planet, your fleet is included into a potential battle against an attacker! Additionally your fleet is visible on a spying probe and the attacker knows exactly what he has to count on.
If your fleet isn't saved, the fleet will be included in any attack taken place at your planet. This could potentially lead to your fleet being fully destroyed.
To reduce the potential loss of your fleet (and your points) it's important to save your fleet as long as you're not able to get OnLine and redirect your fleet. Don't try to hide your fleet behind big defense troops or buildings. In a battle, they will be destroyed first and there is always someone with a bigger and more powerful fleet in the Galaxy.
Most of the time someone is going to attack you it's based on the reason to crash your fleet and get a huge debris field. So therefore SAVE your FLEET all the TIME!!
How to SAVE your Fleet?
Without Moon: Best tactic to save your fleet is sending (deploy) it to one of your colonies. Use your time to arrive with the next time you'll be able to get OnLine and make your next move (use the %age to vary with the speed).
If someone will be able to see your move by using the Phalanx, you still will be able to cancel your arrival on the colony and return to your home planet and therefore it's not possible that another player will destroy your fleet.
With Moon: It's much easier to save your fleet having a own moon available. Your fleet movements are not visible on a and from a moon. So therefore the easiest way to save your fleet is going from your moon to a debris field and use the %age to time the return time with your next available OnLine time.
But just in case ..... There are more saving methods but be aware, none of them is fully secure. There is always a risk, someone else is spying your times and makes potential attacks just in case. But foremost, if you follow those tactics, it's more save then having your fleet standing around on your home planet.