Some Galileo's have problems with continuous reception of the transmitter. First thing is to try it with a different transmitter to see if that might be causing the issue. Borrow a friend's, or have the diveshop trade you one.
If that doesn't help, then consider this... the instructions about how to initiate a dive are pretty specific but rarely followed by users. First, the computer has to be on and then you have to crack the tank (but there must have been at least 3 minutes between the last time pressure was passed through the sensor). Last, make sure that the display doesn't go off before you enter the water, or the computer may have trouble re-establishing the connection. You may want to set the display auto off at 3 or 5 minutes instead of 30 seconds to avoid problems.
What I have found works best is this. I move my gear from the empty tank to the full tank, but don't crack the cylinder. After Donning my gear, and being ready to enter the water, I crack the tank with my wrist at my shoulder near the transmitter. Then within 3 minutes (while the unit is still displaying info) I enter the water. If this doesn't work, then you may have a defective unit.
Do these trials and see what happens. If not, then you can send the unit back to SP/Uwatec. While they advertise that the warranty requires purchase at an authorized dealer, in most cases they will address all customer issues with their products.
I dive with manual gauges on every tank anyway because hoseless integration computers are not yet reliable enough. The value to me is monitoring breathing speed and having it for computerized review to compare SAC and RMV values on dives. But on the dive itself, I stil use my gauges.
Good luck with the tests.