SMD Crystal solder(?) problem and any recommended test procedure
Your layout looks a lot worse in the screen shot than it actually is with the ground pour, however I'd still try to isolate the ground return from the load caps and have it go right back to the ground on the chip. I'd also like to see a ground pour under the caps and crystal (maybe you have one) and connected to the same ground point as the load caps. 

That's not likely your problem- there seems like there are several possibilities. First, the metal case of the crystal may be shorting or there is some PCB problem. Your description tends to indicate not. 

This is an extremely low power-level crystal (100nW drive 500nW maximum drive). Make sure it's well matched to your chip. You can't change the load capacitances willy-nilly if you want accurate timing (+/- 40ppm is required) but make sure they're appropriate (if there are no caps inside the chip they should generally be a few pF less than double the specified capacitance for the crystal- that datasheet shows several possible values for that crystal). You should test the boards for start-up at temperature extremes- marginal startup at room temperature indicates a probable issue related to gm of the chip, and that changes with temperature.   

Finally (and perhaps the best news!), if your assembler is using no-clean flux, and especially if the chip is extreme low power, I'll bet that is exactly your problem. Removing the residue takes a strong solvent and scrubbing. Your re-soldering the parts may affecting the residue and allowing them to start working again. 

Edit: I would suspect the no-clean flux residue- it is extremely difficult to remove. You can also compare the load cap values and specs of the Epson crystal you are using to the crystal used in TI's reference design to see if anything jumps out at you. But also scrub the top of that board in the crystal area with some nasty solvent PCB cleaner and a toothbrush. Solvent alone (even something as nasty as lacquer thinner) is not enough.