Turning it around changes the driven end of the crystal, which in many cases will allow it to oscillate again. IIRC the issue is the TTL oscillator, using a single non CMOS gate, tends to drive the crystal with too much power, and this eventually weakens it. Using a CMOS inverter with a series resistor on the output to the crystal, and a series resistor to the gate input, reduces the drive level to prolong crystal life. You need short traces, low capacitance and attention to decoupling as well, otherwise it is very prone to picking up noise from the supply lines and ground plane, and from sharp signal;s nearby.