It looks like im not completing far enough into the game then, but i could have sworn it stated that the game was saved. No matter what i do when i restart, i always get taken to the square and have to start again. When i head for the 'woman' with the umbrella and follow her through the grid, i just start afresh and not where i stopped playing.
So you go to the grate and follow the woman through and she starts with her long speech about joining her special team? If she isn't doing that every time then you are not starting from square one.
The way it works is as follows:
1. You follow the umbrella woman into the grate and you are taken to the 1st area of the single player. This always happens even if you are 80% through the single player campaign as far as I know.
2. Press X when you are in that area and you will see a map with sectors. Press A on one of those sectors and you will see various points on the map. These are the various portals you have uncovered by shooting ink at them when they were 'invisible'. Press A on one of those and you will travel to it.
The other way is:
1. When you are in the square with all the shops, press X. Go to the 'octo canyon' menu item and press A. that will take you to the same place as following the woman with the umbrella.
2. Follow step 2 above.
What consitutes a level? I worked my way around and transferred to different areas by dropping through grids. I thought id travelled across three but
obviously not if these are levels.
I would be amazed if you were starting again from scratch. The single player is split into sectors. Each sector has a load of hidden portals you shoot to activate. When you go inside those portals there are checkpoints within the level. These checkpoints will be lost if you quit but the whole level shouldn't take more than 5-10 minutes max. When you have cleared all portals in a sector the boss kettle is activated and you can go fight a boss. Kill the boss and the next sector is available.
Literally the only thing not saved is checkpoints within a level (when you go into one of the portals). If you shoot a hidden portal to reveal and activate it, the game saves that and you can warp to that point. You don't need to have completed the level within the portal.
I think you are getting confused because the SP always takes you to the start of the SP maps when you start it up again. Does that make sense?