Did you do a gel cut, or just clean up the original PCR reaction? What was your elution volume and how much of the eluate did you run on the new gel? The original PCR product shows quite a faint band, so my best guess is that between loss of some product during cleanup and presumably not loading all of the eluted product on the new gel, there's just not enough DNA on the new gel to see it.
As for things that could have caused the cleanup to fail....
Check the pH of the binding buffer - if it's incorrect, the DNA won't bind to the column. Most kits include a pH indicator in the buffer for this reason and the documentation should tell you what colour the buffer should be.
Make sure the correct amount of binding buffer was used for the size of the fragment - often small DNA (like PCR products) requires a higher ratio of binding buffer to input sample. If you're using gel slices, weigh them, don't guess the volume.
All pcr purification kits are quite inefficient and dna losses can be high. To minimise losses you can pass your elution buffer/water twice through the column or just do a second elution with more water or you will get a higher yield if you elute with hot ( 70c) water and leave it on the column for twice as long as the kit instructions say. You know that the pcr band is a single band because you cut it from the gel.If you want to know how much dna you have after purification use a nano or other spectrophotometer blanked with elution buffer
You didn't have much product to start with and there is always a substantial loss during clean-up.
I'd suggest setting up several large volume (50-100 microliter) reactions, find the widest gel combs in the lab, pour the gels extra thick, and load all of the PCR reaction into the wells. Minimize the size of the agarose slice & make sure it's completely dissolved before loading in the column. Basically, start with more product so you can end with more.
And as Paul Rutland says, warm up the elution buffer & let sit longer before spinning to get a higher yield.