Hi! Let me see if I can explain this well. I have a hot water pipe in an upstairs bathroom that keeps freezing.

I live in a split level. From the crawlspace, you can see the pipes. The same cold and hot water pipes feed the lower level bathroom, toilet and kitchen sink. The pipes then feed up an internal wall and supply water to the upstairs bathroom. If I am correct, they reach the toilet and then "T" off to the right to feed the tub and the left to feed the sink.

The sink is closest to an external wall. The hot water pipe that directly feeds the sink freezes at 6 degrees Fahrenheit. The cold water pipe that feeds the sink will freeze at below 0 degrees Fahrenheit. The toilet (3 feet removed) and tub (6-7 feet removed) just to the right of the sink never freeze.

I opened up the wall behind the sink and have insulated the pipes with insulation foam, have sealed all the cracks that I could see or feel in the wall with spray foam and then filled the rest of the space with fiberglass insulation for good measure. I could feel cold air coming into the space and it was greatly reduced after I did all of the insulation work. I sealed up the wall and re-installed the sink.

Well, it dropped below 6 degrees the other night and it froze again. Again only the hot water pipe.

Inside the wall, the hot water pipe is only 4-6 inches removed from the cold water pipe.

For the life of me, I can't figure out why it is freezing.

Any ideas?

If these are copper pipes, the cold could be conducted (actually the heat is removed) through the piping from below where you are insulating. Since you have a crawl space, why not put a small heat tape on the pipe that freezes and then wrap with insulation. Close up all openings in the crawl space.

A hot water pipe will usually freeze before cold because there is more air in the hot water. The cabinet, with the doors closed, will restrict warm interior air from reaching the wall.

What kind of pipes?

Is this the bathroom lay out you are describing with the supply pipes coming up through the interior wall behind the toilet?

Scientists have proven that hot water does not freeze faster than cold water, although, a hot water pipe may freeze before its neighboring cold water pipe. This is sometimes due to location, usage, or exposure.
Insulating a pipe in an enclosed, exposed area is not enough to prevent it from freezing - insulation alone does not provide heat, and, will insulate the pipe from any heat source. Heat tape is an option, but should never be used in a confined space, and, will not provide any protection in the event of a power outage.
It is always beneficial to turn your heating thermostat higher in anticipation of colder outdoor temps; sometimes just having a warmer area is enough to keep nearby piping from freezing. When it is not possible to gain access to properly insulate / seal the pipe chase way, it may help to open cabinet doors, as hkstroud has mentioned. You can also cut in a louver to allow warm air into the cold area - louvers are available with an adjustable damper that can be left closed during all but the coldest weather.
As a last resort, you can keep the basin faucet trickling; moving water is less likely to freeze, and you will know if / when it does freeze, however, trickling water can present another set of undesirable consequences.
The best action would be to re - route the piping away from any cold, exposed area, and it may be possible to install isolation valves with drains; this would allow you to drain the piping that is subject to freezing...

Mpemba Effect

Very good, hkstroud, I stand corrected on my very broad opening statement, however, this phenomenon applies to water under atmospheric conditions. Water contained, and, under pressure is not subject to evaporation, air currents, relative humidity, water column exchange, or radiational cooling...

And besides, I'm only a plumber, how much could I know?