Word for someone who can't keep up with the times?

Reactionary: someone who opposes political or social progress or reform. Highly conservative and favours a return to an earlier, more disciplined, social order.

[Sources]: Oxford Dictionaries; Wiki

Diehard (variant spellings): first used on the battlefield in the mid C19th, then to describe Conservative politicians who were clinging to British imperial power in the 1930s. Now refers to someone who is staunchly opposed to change, even when there are good reasons for it.

[Sources]: Oxford Dictionaries; Wiki; The Diehards

Sometimes the term "luddite" is used when speaking about someone who refuses to use new technologies or methods, despite how convenient or labor-saving they may be.

A non-negative term I've heard people use to describe themselves or others is "old-school."

Sounds to me like the word "Conservative" fits very well with what you are describing.

Other single word synonyms:

• Traditionalist
• Orthodox