This may sound like a strange problem and it's certainly confusing me. I built a binary clock following this design, initially I built it on breadboard and it worked perfectly for a couple of weeks. I plan to build a clock in a case with it but since i've moved it onto stripboard the buttons haven't worked right. Initially they seemed to work ok but the first time i showed it to someone, the buttons started misbehaving, pressing one would advance both sets of LEDs, turning the LEDs on and off would change the time entirely... as if the input was floating maybe, but the switches are connected using pull up resistors (I think, I'm new at this...) so it shouldn't be an issue.. I rebuilt the switch circuit on the breadboard and it once again worked fine, then i redid it on the stripboard, exactly the same circuit and it worked the first time I tried it then started misbehaving shortly after. I've just turned it on again and it seems to be behaving, I'll wait and see what happens..
Aside: Are you debouncing your switches?
In general strip board is more reliable than breadboard.
So I think this is down to you not building it correctly on the strip board. It sounds like you are missing the +5V on the pull up resistors. Use a meter to see if you have the correct voltages on your strip board version.
I've replicated the circuit exactly as it was on the breadboard, 5v to the 3 resistors which go to a trace each which has gnd connected through the switch and a wire going off to the arduino. I don't think i have any debounce but I certainly do have 5v to the resistors, i've checked various bits like that to no avail. I know the code is good cos it works on the breadboard, likewise for the circuit.. Naturally it's working perfectly now... I'll keep playing as see if it breaks.
Might I suggest debouncing your switches the next time you have a problem.
It won't take you more than a few mins to quickly add this to your sketch and if the problem disappears then you'll know why. http://www.arduino.cc/playground/Code/Bounce
Thanks everyone for your ideas, I think it was probably down to a not quite perfect joint on the 5v line, it's been behaving since I re-did it... Grumpy_Mike got it in one ;) I was expecting a short based on what it was doing but as I'd been reading and posting this I'd tried disconnecting the 5v and got the same result! Now I just have to squeeze it into the box..