Good question! I have absolutely no idea how the thinness would be affected over the long-term, but even if it did hold up great, the lid concerns me because it's not a secure, tight-fitting/air-tight type of lid, such as a screw-on lid. I'd be afraid of the container either getting knocked over and the lid popping off, or of the lid letting enough air get inside over time, thereby weakening the concentration.
If it were me, I would be on the lookout for small, 10 oz. (#5) bottles of liquid laundry detergent (they make them that small for a doing a couple of loads of laundry). Re-claimed liquid detergent bottles with a secure, tight-fitting lid with a no-drip spout (most of which are made of heavy-duty #5) are perfect for the task. That's what I store mine in, only I use a bigger size- big enough to make about seven or eight 2.8 lb. batches. My solution holds up pristinely in such containers for well over a year (and counting).
IrishLass