Why is solid phase peptide synthesis limited to 70 amino acids?
The issue is one of yield. Each step has a certain yield percentage of yield, that the synthesizers will maximize as much as possible. However, given that it is fairly impossible to generate 100% yield all the time, the amount of desired protein you get over time will deteriorate exponentially with length.

For example, say that each step gives you 95% yield. If you have a protein that is ten amino acids long, your final step will give you .95^10 yield, which is about 60%. 

However, with the same yield per step, but a 70 amino acid chain, the amount of protein you want drops to 2%.

Even if you are at 99% yield per step (a difficult feat), your final yield will be under 50% for a 70 amino acid chain.