There are three main single-stranded DNA repair mechanisms.

The first is nucleotide excision repair. In this mechanism, specific endonuclease enzymes remove nucleotides containing damaged bases. DNA polymerase then replaces the region with undamaged bases, and ligase seals the addition with phosphodiester bonds.

The second mechanism is base excision repair. In this mechanism, glycosylase enzymes detect and excise damaged bases. DNA polymerase then replaces the region with undamaged bases, and ligase seals the addition with phosphodiester bonds.

Finally, there is mismatch repair. In this mechanism a new strand of DNA is tested for pairing with the template strand, prior to methylation. Any mismatched nucleotides are removed, replaced, and joined into the complete strand.

Telomeres are regions of non-coding DNA at the ends of the DNA strands. The telomeres function as regions of acquired damage and mutation, protecting the actual genome. Telomerase is the enzyme responsible for adding additional nucleotides to the 3' end of the chromosome to maintain the telomere.

Helicase unwinds the DNA helix and separates the strands to form the replication fork. Primase synthesizes short RNA primers on the DNA template to help recruit DNA polymerase, which then adds nucleotides to build the new DNA strand.

Helicase is one of the first proteins necessary for initiating DNA replication. It is responsible for unwinding the DNA double-helix and separating the hydrogen bonds that hold the two strands together. This allows DNA polymerase to enter the replication fork and recruit nucleotides to build daughter DNA molecules.

Single-strand binding proteins attach to the DNA in the replication fork to prevent it from reannealing. Topoisomerase breaks phosphodiester bonds in the DNA backbone to relieve tension, while DNA ligase reestablishes these bonds after replication is complete and fuses Okazaki fragments on the lagging strand.

The origin of replication is the particular sequence in the genome where DNA replication begins. In prokaryotes, there is a single origin of replication, whereas there are multiple origins of replication in eukaryotes. At the origin of replication in eukaryotes, certain proteins bind to form the origin recognition complex. This complex is then used to recruit replication proteins and initiate the process of DNA replication.

DNA polymerase III is the main replicatory polymerase in prokaryotic cells, responsible for synthesizing daughter DNA strands during replication. DNA polymerase I performs more specialized functions, such as synthesizing DNA during DNA repair pathways.

The difference between an endonuclease and an exonuclease is whether or not the cleavage takes place in the middle or at the end of a strand, respectively. DNA polymerase III is cleaving bases at the end of the strand, meaning it has exonuclease function.

Single-strand binding proteins, as the name suggests, bind single-stranded DNA. This is important because it helps prevent the strands from reannealing prematurely. These proteins are essential for maintaining the replication fork.

Helicase is responsible for separating the strands at the replication fork, but is not directly responsible for preventing single-stranded DNA from reannealing. It creates the replication fork, but is incapable of maintaining it. DNA topoisomerase cuts the DNA backbone ahead of the replication fork to avoid topological problems. Histone proteins are removed during DNA replication, and are not involved in this process. 

Since the strands can be successfully "unzipped" from one another, this suggests that DNA helicase is working just fine. There is also nothing in the prompt that states the synthesis of new strands is not working, so DNA polymerase is fine as well. The problem involves keeping the strands separated for a long enough time. This is the job of single-stranded binding proteins. Because of this, we can argue that this protein is mutated in the cell.