Hello Claude,
I also have a CPC Deluxe HD GPS mount that I use very extensively from home for my planetary and lunar work. Yes, you need to do a star alignment every time you switch on the mount.
The mount will not know if you had taken it down and set up again. It also cannot assume that you had not changed the position of the scope between set ups, say by unlocking the clutches to align the finder scope. Also there are small errors in the functioning of most mounts, and over the course of a night you will see the goto accuracy diminish slowly. If you've been using the mount for several hours, it is not uncommon to even do a new alignment process to reset the mount.
Really it is not an onerous process to do a two star alignment. I certainly don't find it so, and I know that if I take my time to do a very accurate alignment that the goto can be very accurate so as to leave the object centred. By also doing an alignment every time, I make sure that the goto is functioning at its very best accuracy and best tracking quality.
For what it's worth, I align the finder first with a 25mm eyepiece and fine tune it with a 5mm. I then carry out the two star alignment with the 5mm, but with the image of the star as a very large doughnut as this doughnut is very easy to gauge when it is centred in the field of view of the eyepiece. I find this method to be very quick and very, very accurate. This is just one way of achieving a good alignment accuracy. The more care you take with the alignment, the better the results will be for you
Some mounts do store the final position of the mount (such as the Park Position), but unless the mount/handset has a built in clock that keeps running while the mount is switched off, you will find that nearly all mounts will require some sort of input from you, be it time or date or location. Even if it stores the location, it will still ask if you are using that position or a different one. The CPC mount does not have a final Park Position, so it cannot store such alignment details.
By the way, my CPC is a modified one! It came from an 1100 Deluxe GPS like yours. I got the mount without the scope (the original owner had deforked the OTA), and I removed the non-mechanised arm, fit a dual Losmandy/Vixen dovetail clamp to the other, and the CPC mount is now a monster one arm mount! The single arm mod is even strong enough to take the original 11" scope. My CPC takes a 9" Mak which is as heavy as an 11" SCT. I had looked at the Evolution mount that can also take a 9.25 SCT, but the arm is not long enough to take the 7" or 9" Maks I've used. The arm length is significantly longer of the CPC 9.25 and 1100 (same arm length mounts).
Another CPC tip: A two star alignment also has its limitations for goto. If you find that the accuracy is not as good as you hoped, don't forget about the "Precise goto" function. It will ask you to select a bright star that is close to the object in question (the handset will present a series of named stars in increasing distance from the object). You hit the goto button and the mount will move to that star. You then centre the star in the scope, re-hit enter, and the mount will then move to the object with incredible accuracy. I found this function very useful when I did my planetary nebula marathon a couple of weeks ago, as some of the PN's were very, very difficult to identify if the goto was not so accurate. It took me a little while to get used to it, but now find it a very handy ace card when I'm struggling to spot a very difficult object