Once you have collected a one-way HEx ticket from the machine, you must use it within 3 days. However, it stays in the system for SIX MONTHS from the original date you order it for.

If you are travelling on the HEx at any point between now and December, you can book a ticket before June 30th for 25% off using VIRG25. Book the ticket for travel on 29th June, even if you are travelling in October. The ticket will stay in the system until 29th December, at which point it will be lost.

I did this recently using the 'free first class upgrade' promo which ended in May. I booked a ticket for travel in May but didn't collected it until some point in June. The ticket popped out of the machine just fine.

Here are the exact terms:

For up to six months after you book them you can collect all online tickets from Heathrow Express ticket machines.
Express Class & First Class Single
Valid for three days after collecting them from a ticket machine.
Express Class & First Class Return
Valid for one calendar month after collecting them from a ticket machine.