Electronic – Using Buck Converter as Solar Charge Controller ? (see pic)

Is your lab power supply limiting the current to match what your solar panels would provide under your test conditions (i.e. not max rated current on the panel, but what the current is when it's dropping from 7V to 1.5V)? Could be that your solar panels don't provide quite enough current and voltage will sink since load resistance does not change.

Easy way to check is to hook it up to your power supply and slowly reduce the current via the current knob.

If you have a really simple supply and can't control the current, then you're going to have to us a multimeter to check.

EDIT: OP has provided the follow quick schematic in comments: http://i.imgur.com/m8S8Q4j.jpg

While in some use-cases, you might want to do this, generally it's better to have some form of regulation and predictable behaviour. Because there is a large variance in the output of a solar panel, it's generally better to store solar energy into some form of a power reserve first (battery, large capacitors, etc.) and then using that to power your load on-demand.

When your energy source is a solar panel, the constant current is not constant, as it depends on how much current your panel delivers.

This way, the "constant current - constant voltage" charging algorithm transforms into "limited current - limited voltage" charging. Batteries are generally OK with this, as long as your BMS behaves.

The load will subtract from the available charging current and it is up to you to get large enough solar panel if you want the batteries to be fully charged at the end of the day.