Should I discontinue use of Tri-luma when my pigmentation is gone or wait the full three months?

Melasma is a persistent disease, if you stop the medication, it may come back, discuss it with your family doctor or dermatologist. You may be able to reduce the frequency of topical application.
Regards, 

Ideally you can decrease the dose or application frequency to find the least amount of days per week you need to apply the topical. As a guide most dermatologists will cycle HQ 6 months on and 2-3 months off. Melasma can not be completely cured, however effective treatment are possible. Melasma patients have skin that is very sensitive to UV light. Even the smallest amount can stimulate your pigment cells to produce colour. The mainstay of treatment is strict UV protection- hats, sunglasses and SPF every 4 hours. 
I prefer to use a combination of creams and laser for melasma. My most frequently prescribed topicals include hydroquinone, along with vitamin A creams and botanical extracts. The exact percentages will depend on your skin sensitivity, clinical presentation and your current skin care routine. 
I usually start my patients on a series of lasers (low dose Q switch or Picosure), along with medical therapy. Another laser I use is the Clear and Brilliant in the Permea setting. In some cases I combine glycolic AHAs, TCA low strength single coat peels, and in other cases I use a tablet called Tranexamic acid to help modulate the blood vessels that are associated with melanocytes (pigment cells). Melasma treatments should be tailored to each patient. 
All the best, Dr Davin Lim. Laser, surgical and aesthetic dermatologist. Brisbane, Australia. Cutis International

Thank you for your question. I'm glad to hear that you are experiencing positive results with Tri-Luma cream. In my experience, once melasma resolves, then treatment could be stopped; however, recurrence rates of melasma are high. I highly recommend you consult with a board certified dermatologist to have your skin evaluated and to discuss options moving forward. Take care and good luck.