The reasons for shoddy reproducibility are p-value hacking, intense pressure to publish at all costs, and a premium on 'gladwellesque' results where a simple theory seemingly explains a lot.
Gellman and Uri Simon-Johnson have both written a lot about this.
Having watched scientists at work, reproducing 10 of 13 high-profile studies sounds pretty reasonable. Given p≤0.05, you'd expect 19/20 to be reproducible. Then you add in other factors:
- Surprising positive results get published more readily than negative ones.
- Some results may be sensitive to tiny changes in methodology.
- And more: "Why Most Published Research Findings are False" http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1182327/
Some of these effects can be reduced with pre-registration of studies, and with other methodological improvements. But in general, even when everybody plays by the rules, a fair bit of garbage is going to slip through, because it's hard to eliminate all sources of error and bias.
So when a scientific field can say, "Hey, 3/4ths of our really interesting results are real!", that's about what I expect when the processing is working.
No, that's not the case; follow your link to "Why Most Published Research Findings are False" to see why that's not the case. The "positive predictive value" of a discovery, even without any bias, is very different from what the p value would imply.
It also raises the question of whether the reproducibility study is itself reproducible.