Charging Li-ion batteries in parallel

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I wanted some opinion on my set up here, just to make sure I got the basics right.

I have a Li-ion battery charging circuit based on the MCP73113. This is designed to be a single-cell battery charger.

The battery itself (3.7V, 650mAh) comes with its own PCB with Schottky diode and current regulators as protection. EDIT: Not a Schottky diode. Current limiter and a Protection IC.

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By design, they work together just fine.

I have more batteries from the same manufacturer and wanted to make higher capacity packs by putting two cells in parallel. The two cells come with their own PCB, but I only kept one of them, as I soldered their leads together. It seems to work and they are charged and discharged just like regular batteries (3.7V, now 1300 mAh).

However, not all the packs I made work smoothly and I get a failure rate of 2 in every 10 packs. They all start out normally, but occasionally when the batteries are not charged for some time, or are used up, they tend to not work anymore. So far, in only 1 pack I found the voltage to be different (both now below 2V, aka dead).

I assume my method is not the right approach to ensure 100% success rate, so I was wondering how can this be solved. All the controllers I looked into was designed for multiple cells in series, not parallel. Am I fundamentally missing something here?

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