In general, inkjet printed photos will fade faster than commercial fabrics when washed as often as you describe. I always tell people that inkjet fabrics are washable "to a point". If you treat them as you would a delicate fabric, then it would most likely be OK. But that's not what you've described.
If you have an HP printer, you can lengthen the life of the print by adding fabric softener to the rinse water, but the prints will unfortunately still fade faster than the commercial fabrics. Also, the HP inks are dye-based (not pigment), so they will be more susceptible to fading from light.
If you have an Epson printer with DuraBrite (pigment) inks, I have had very good luck washing the EQ Printables Cotton Lawn. Yes, that is a very specific ink/fabric combination, but I think there is something about how smooth the fabric is that helps the pigments to adhere to it. If you then spray a 1:3 ratio of FabricMagic* to water on the print, let it dry and heat seal it (medium heat since high heat causes the DuraBrite inks to yellow), I think that is probably your best chance at getting as permanent a print as possible. The FabricMagic will change the hand of the fabric some, but it may be worth it for the increased longevity of the print. I should mention that my testing involves washing a print 5 times. In my experience, most fabric/ink combinations show marked degradation in just five washes. The combination I mention here showed almost no degradation in my testing, though I did start to see a little bit, so it's not a perfect solution.
The other thing that will make a huge difference in the life of the print is the detergent you use to wash the quilt! I have tested washing inkjet prints in a few different detergents and have settled on Synthrapol as the most gentle. Definitely stay away from any detergents that contain bleach or brighteners (such as Tide)! But I've even had trouble with Woolite for Darks which supposedly contains neither of those. I would say that if the person you are giving the quilt to hopes to just throw it in the wash without thinking about it, do
not include an inkjet print in the quilt. They really do need to be treated with special care.
*FabricMagic is a fixative that was designed to be used with colorants and painted/stamped/stenciled onto fabric. I decided to try using it as a post treatment on inkjet fabric.
It has not been successful on all fabrics, but I was pleasantly surprised with the results when I used the Epson DuraBrite inks on EQ Printables Cotton Lawn inkjet fabric. That said, I have not washed any of my test prints more than 5 times, so
your mileage may vary.
FabricMagic is made by
Earth Safe Finishes. I have no affiliation with this company - or with EQ for that matter. I'm just always looking for solutions to make inkjet prints more washable and this definitely shows promise - though to be really thorough people all over the country would need to test this since different water supplies can make a difference too.