In the years since Miller's work, many variants of his procedure have been tried. In solution, hydrolysis of a growing polymer would soon limit the size it could reach. Abiotic synthesis produces a mixture of L and D enantiomers. Each inhibits the polymerization of the other. Link to a discussion of enantiomers.
All metabolism depends on enzymes and, until recently, every enzyme has turned out to be a protein.
The synthesis of DNA and RNA requires proteins. So proteins cannot be made without nucleic acids and nucleic acids cannot be made without proteins. The discovery that certain RNA molecules have enzymatic activity provides a possible solution. While no ribozyme in nature has yet been found that can replicate itself, ribozymes have been synthesized in the laboratory that can catalyze the assembly of short oligonucleotides into exact complements of themselves. In principal, the minimal functions of life might have begun with RNA and only later did proteins take over the catalytic machinery of metabolism and DNA take over as the repository of the genetic code.