The kink that Will has pointed out would be enough for me to want to replace the spring as it is a potential breaking point; however, I don't think that he spring is "set". The main coils look well spaced and it has a healthy reverse coil on it, so I would be surprised if it's not providing enough power. Also, I believe that a lack of braking grease is likely to result in the mainspring failing to slip rather than slipping too early. The way that braking grease works is that is holds against the shearing force between the bridle and the barrel wall, allowing the spring to be wound up, until the shear force reaches a certain strength, and then it allows the spring to slip. As it slips the shear force reduces to below the braking limit and the bridle once again grabs the barrel wall. I could be completely wrong on that though :-)
Try winding the mainspring by hand (use a screw driver in the ratchet wheel screw on your Seiko as I don't think it has manual winding) and see if you can feel when it slips. If you can get just a couple of turns on it then that should be enough power to run for considerably more that just a few minutes.
When you reassembled the movement after cleaning it did you test the free running of the train without the pallet in place? A puff of air on the escape wheel should be enough to spin the whole train easily, and a couple of clicks of power on the mainspring (again use a screw driver to turn the ratchet wheel) should spin the train first of all the right way, cause the train to overshoot the springs fully unwound position, and then recoil in the opposite direction for a couple of turns of the escape wheel (or more).
If the train won't spin with a puff of air or there is no recoil then you need to strip the train back and reassemble one wheel at a time, each time testing the freedom of the train for power loss until you find the problem, which could be anything from a bent pivot, broken jewel, incorrect end or side shake, damaged wheel or pinion teeth, etc, so it is important to always thoroughly inspect every part after cleaning and before installing it.
If everything in the train is free enough to see recoil from a couple of clicks on the ratchet wheel then reinstall the pallets and put about half a turn of power on the ratchet wheel. Now by just very gently nudging the pallet fork from side to side with the tip of a clean oiler you should see the pallet fork snap smartly across to the opposite banking pin. Also, if you stop nudging the pallet fork just before it snaps across and take the oiler away, the pallet should return to the banking pin you were nudging it away from (this is called draw).
If it doesn't snap across or draw back then carefully inspect the pallet stones for any chipping or damage, and the pallet arbor pivots and jewels.
If it does snap across nicely and draw back properly, then the issue is likely in the balance assembly.
I hope this helps.