I have an older CJ 500 converted to solvent so my pump set up might be slightly different.
Find the lines that run from the capping station to the pump. Remove the lines (should be white tubes) from the capping station. Then get a syringe that will fit inside the white tubing. Using some cleaning fluid, force the fluid through the line ( one at a time) and watch the drain lines in the drain bottle. Watch out as you pressure up the line as it might squirt some fluid back at you around the connection of the syringe and tube. Hold some paper towel around in case. You might feel some resistance as you push the fluid through but you should see it come through the drain lines. When it it blocked it might take a bit of time for the cleaning fluid to break down the chunks in the lines. On my CJ 500, it does not wake up to do a cleaning so I often need to clear the drain lines. It’s just part of my cleaning procedure.
Also on my capping station I have a set of clear lines that should not have any ink in them and the odd time they do get back flow in them and then plug. These clear lines need to be clean in order to recharge the heads with ink as it prints. If you ever get drop out after printing a large print after a foot or two into the print ( ink starvation ) these clear lines are one possible cause if they get blocked.
Also again make sure you have a good seal on the capping station and no chunks around the rubber edge that might stop the heads from sealing. By using the syringe and a small piece of the tubing attach to the capping station and while the heads are parked, draw ink through the heads and capping station into the syringe. If you hear air leak or see a lot of bubbles in the syringe with the ink you have an air leak some place.
How are the ink cartridges for ink level. I have also heard that when carts are low they can cause a back flow and suck the ink back into the cart enough to dis charge the heads. With the syringe you can get ink back into them quicker and do the above method.