Hi welcome to the forums, and to the TR.
Like you say it seems odd because normally you’ll loose the time & date altogether it it’s bios battery. It wouldn’t hurt to reset it though by disconnecting the bios battery.
Here is my walkthrough on how to get the TR apart, you wont need it all for bios battery, but thought it was worth giving it all. just follow the yellow text only to remove the keyboard
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Remove Battery, Lay laptop on its lid upside down on a soft cloth or soft towel.
take out all screws you can see note the two under the battery are shorter (don’t get them mixed up when you replace)
there is another screw under the ram cover and, remove the two screws that hold the keyboard in under the rear rubber feet, (also small ones)
when all screws are out turn laptop over carefully.
use a thin screw driver or pick to lift the top right corner of the keyboard just a little (hook it carefully under the delete / break key)
lift it just enough so you can hold it lifted with your finger now while holding it use the thin screw driver or pick to release the two catches above the F11 & F6 keys. (if you can’t lift the keyboard don’t force it but check you have removed the two screws under the rubber feet).
Keyboard should now be loose. remove it enough to undo the connector the brown catch needs to be lifted with pick or thin screwdriver.
There is a connector just below the keyboard one that is a push / pull fit and one more screw not quite top left corner under where the Tab key would be when assembled.
The top cover / palm rest should come off now but you may have to wiggle it gently as there are a few clips on the front. Don’t force it. If it wont come off you have missed a screw somewhere:-
You should have 14 screws total.
1 short / medium (ram cover centre rear)
4 short, (2 for keyboard under rubber feet, 2 under battery).
9 long (7 in casing rear, 1 in ram compartment, 1 under tab key)
With top / palm rest removed the rest should be pretty obvious..
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The above is how I do it but some of this is detailed on the forums with pictures so have a look there, (hdd replacement topic)
http://www.siliconpopculture.com/forum/viewthread/5486/
Before starting make sure you are earthed no static, and you’ll need jewellers screwdrivers or similar, a set of snap-on picks are useful to.
On reassembly don’t get screws mixed up, long ones where short ones go can damage the casing.
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With keyboard removed the bios battery is alongside the bottom edge of the heatsink fan, and is plugged in to the mainboard near the hetsink fan if you can tell which is which uplug both for 10 seconds or so.
Before trying the above go into the bios and set the time and date there. Also change something else like boot order or volume so you can see if it gets reset later. Hit F2 when booting just after vaio logo, (If it asks you for a password that’s not good)
Don’t think that bios battery on eBay will fit / is compatable, but I have good used ones if you need one..