A couple of things - the first is that I often hear people say that you should strip off/remove the pre-seasoning that comes with skillets, as it is inferior or will interfere with a proper seasoning done by you. Since you are having issues with your current seasoning, and it's not getting better, it might be best to strip it away and start from scratch.
While one might think that soap and a scouring pad is an okay to remove seasoning, soap is going to leave a residue. Cook's Illustrated/America's Test Kitchen (the closest thing to an encyclopedia or the Burning Bush for all cooking-related matters) says that a great way to remove existing seasoning is to run your oven through it's self-cleaning cycle with the skillet in it.
If you do not have a self-cleaning oven, here is another article from Cook's Illustrated on how to do it with oven cleaner, soapy water, steel wool and vinegar -
Follow this method to completely remove any residual seasoning on a cast-iron pan before reseasoning it. Easy-Off Oven Cleaner is a caustic alkali, so be sure to work outdoors, wear rubber gloves, and avoid spraying near your face or skin. The skillet will rust instantly once you’ve discarded the vinegar-water solution and rinsed and dried the skillet in step 5, so be sure to immediately apply oil to the surface.
- Working outdoors, place concrete block on ground and cover with heavy-duty kitchen trash bag, draping bag over block so that sides of bag will be easy to grasp and pull up over skillet.
2A. Place skillet upside down on top of block. Wearing rubber gloves, spray skillet all over with Easy-Off Oven Cleaner, being careful to keep spray away from your face and exposed skin.
2B. Flip skillet over and spray inside.
2C. Pull plastic bag up and around skillet and tie to close. Leave wrapped, sprayed skillet outside (or in garage) for 24 hours.
3A. Wearing rubber gloves, remove plastic bag. Scrub skillet all over with steel wool and hot soapy water to remove all residue.
3B. Rinse, repeat scrubbing with steel wool, and rinse again.
Combine 2 cups distilled white vinegar with 2 cups water. Fill skillet with vinegar solution and let stand for 30 minutes to 1 hour.
Discard solution in skillet. Rinse skillet well, then dry well with paper towels.
(start remaining seasoning process, below, here)
Cook's Illustrated: How to strip a cast iron skillet
Once you have, basically, the unseasoned metal skillet, if you want state of the art seasoning, go and find food-grade flaxseed oil. Flaxseed oil is the base for linseed oil, which is used as a tough, durable furniture finish. Keep in mind, you MUST get food-grade oil, as furniture linseed oil has a lot of toxic chemicals added to it.
Google shopping search for food-grade flaxseed oil
The flaxseed oil so effectively bonded to the skillets, forming a sheer, stick-resistant veneer, that even a run through our commercial dishwasher with a squirt of degreaser left them totally unscathed. But the vegetable oil-treated skillets showed rusty spots and patchiness when they emerged from the dishwasher, requiring reseasoning before use.
Why did the new treatment work so well? Flaxseed oil is the food-grade equivalent of linseed oil, used by artists to give their paintings a hard, polished finish, and it boasts six times the amount of omega-3 fatty acids as vegetable oil. Over prolonged exposure to high heat, these fatty acids combine to form a strong, solid matrix that polymerizes to the pan’s surface.
Once you have your food grade flaxseed oil, here are the steps:
How to Season Cast Iron with This Method
Although lengthy, seasoning with flaxseed oil is a mainly hands-off undertaking. We highly recommend the treatment:
- Warm an unseasoned pan (either new or stripped of seasoning) for 15 minutes in a 200-degree oven to open its pores. The best way to strip a cast-iron pan of seasoning is to run the pan through your oven's self-cleaning cycle.
- Remove the pan from the oven. Place 1 tablespoon flaxseed oil in the pan and, using tongs, rub the oil into the surface with paper towels. With fresh paper towels, thoroughly wipe out the pan to remove excess oil.
- Place the oiled pan upside down in a cold oven, then set the oven to its maximum baking temperature. Once the oven reaches its maximum temperature, heat the pan for one hour. Turn off the oven; cool the pan in the oven for at least two hours.
- Repeat the process five more times, or until the pan develops a dark, semi-matte surface.
I'm going to assume that warming the skillet in the oven only set to 200 degrees, and then turning the oven off, and leaving it open while applying oil will have the oven cool enough to move to the next step. Also, saying to "repeat the process" does not include stripping off the existing seasoning each time. Just repeat the actual seasoning part.
This method was originally put out there by a blogger named Sheryl Canter. I don't think ATK added any twists of their own.
Sheryl Canter's blog entry about seasoning/polymerizing your skillet
Cook's Illustrated how-to article, NOT behind their paywall
All of my quoted passages are from the Cook's Illustrated articles.