Once infected with a std/sti, how long can you leave it untreated? Will it cause infertility?

It depends. Some stis such as chlamydia and gonorrheas cause infertility and should be treated asap. Others such hpv and herpes generally do not affect fertility but that does not mean they should necessarily be ignored.
Don't wait! Why wait? If you think you might be infected, then get seen and get treated. There is no good reason to wait. True, some infections can clear on their own, but many others will not and some will progress to severe problems such as infertility, or even death.

Related Questions

Once infected with a std/sti how long left untreated can it cause either infertility or other problems?

Depends which STD. Also depends upon gender. I.E. Hiv?Aids does not impair fertility until subject is bebilitated from their diease. Syphilis, hpv & candidiasis do not significantly impair fertility. Trichomona and chlamydia infections are major causes of female infertility in women, if not not treated early and they develop pelvic inflammatory disease (pid). Less likely in males. Same 4 g0norrhea in both sexes. Read more...