Lives malfunction

Just get the Lives from the Mailtoad first (5 lives for Mario, 20 lives for Luigi). Nobody really knows why Nintendo did this, but sadly, we have to live with it.

The way I get lives is just play. From time to time, you will collect lots of star bits, maybe coins, and find a few lives here and there. Since Mario's health is only 3, you might need at least 10-15 lives and find a Mushroom that can give you 3 extra health points in every level, except when you have to do the Daredevil Comets, which really aren't that bad once you get used to it. The Lava Galaxy in the Last Dome: The Garden is the only problem, since in this Daredevil Comet, you have to survive through a course of one of the previous Stars you played in the Lava Galaxy. Just don't rush on that one.

Except for the Mailtoad part giving you some extra lives, this basically also happened in Mario's two previous 3-D platfomers, Super Mario 64 (Nintendo 64) & Super Mario Sunshine (Nintendo Gamecube). No matter how many lives you had when you last saved, if you shut down the system and start it back up, you start out with just a few lives. I do not know why Nintendo programmed it this way, but for Super Mario Galaxy, it is pretty easy to regain the extra lives. At the Comet Observatory, there are several extra 1-ups. Here are the ones I know of:
1. Break the box at the "Garage" with a spin or a ground pound.
2. After restoring power to the "Kitchen" area, go behind the "Kitchen" and
there should be a 1-up under the stairs.
3. After unlocking the Red Star powerup, you can fly to the top of the
Observatory and there should be a 1-up near there.
4. After unlocking the Red Star powerup (might not be necessary, but makes it
much easier), you can fly under the "Library" area, and there should be a
1-up near where the green, rotating platforms travel.
These are all of the ones that I know are in the Comet Observatory, but there might be more that I do not know of. Also, many galaxies contain a few 1-ups each time you visit them. Also, if you go to any galaxy, then return to the Comet Observatory, all of the 1-ups (exception being the five from mailtoad's Princess Peach letters) will reappear, even if you just breifly visit another galaxy.

The game automatically resets your lives to four whenever you start playing. There is nothing you can do about it except pick up the lives that are around the observatory. I know this is a pain though, I once had over 20 lives and had to stop playing.

It's automatically like that. It's no malfunction. Although I do wish you could save your lives. Just find some 1-ups around the observatory, ask the Mailtoad if he has any letters from Princess Peach. Get the 1-ups. You can also (if you unlocked the Garden dome already) go to Deep Dark Galaxy and get all the 1-ups there.

Sadly, lives aren't cumulative, so you'll always start with 4 lives... Once I collected 99 lives, and they all were gone, what a waste of time!
Hope I helped!

I really don't know why Nintendo takes your lives away but we have to live with it. Mailtoad will usually give you 5 lives anyway, so you'll start with 9 lives, just like a cat. But yeah, every time you have to start with 4 or 9 lives.