Is it possible for vulvovaginal candidiasis to cause infertility?

No. Factors that cause infertility affect ovulation, sperm parameters or tubal patency. Vulvovaginal candidiasis is not a cause for infertility.
No, unless. .. Most women have had candida "yeast infections" but they don't affect fertility. Rarely, an underlying medical condition can cause frequent infections - diabetes, or autoimmune disorders needing steroid treatment. Autoimmune disorders may be associated with recurrent miscarriage or infertility. Diabetes does not cause infertility but if poorly controlled increases miscariage and birth defect rates.
Maybe. Sperm like a slightly alkaline pH and vaginal yeast infections can alter this pH to the highly acidic side.

Related Questions

I need help managing chronic vulvovaginal candidiasis. I take fluconazole when I have an infection but I get up to 7 infections a year! Help!?

Verify the organisms. It is reasonable to obtain a genital dna probe analysis for yeast and bacterial infections. Not a test for everyone, but with your history it is appropriate to assess what you are actually treating. Also consider using gelatin capsules 2 times weekly filled with boric acid and placed vaginally with lubrication to maintain the appropriate acid base status. Also check an HIV test.
Infection. One option you have would to change your medicine or take the Fluconazole every day.