I would recommend adding some CYA. The easiest way is to use dichlor, which adds BOTH chlorine and stabilizer. If you have access to a Sams Club, they have excellent prices on undiluted dichlor. You may find it elsewhere: look for product that shows at least "56% available chlorine"

. . . membership upgraded.

Undiluted dichlor is getting hard to find, but is available at Sams Club and via Amazon. It's sometimes available at Lowes or Home Depot, but you'll need to be a expert label-reader to recognize it!

PoolBrand granular dichlor 50lbs @ Sams Club => ~$2.20/lb (May 2014 in Chattanooga)
PoolBrand dichlor bagged shock 24lbs @ Sams Club => ~$2.50/lb (May 2014 in Chattanooga)

Kem-Tek dichlor 22 lbs @ Amazon => ~$3.50/lb (May 2014)
Kem-Tek dichlor 12 lbs @ Amazon => ~$4.10/lb (May 2014)
Kem-Tek dichlor 5 lbs @ Amazon => ~$5.00/lb (May 2014)
Kem-Tek dichlor 2 lbs @ Amazon => ~$9.00/lb (May 2014)

Keep in mind that Amazon products normally ship free; and that in many parts of the country, you will not have to pay sales tax. Shipping + tax can increase the cost from other suppliers by 15 - 40%, so compare delivered cost, not nominal price.