Why is it important to conduct an experiment more than once?

If you are using statistical analysis (and you are using it honestly) then it is understood that there is a small but finite possibility (usually 5%) that you obtained your significant results by chance alone. So replication of studies helps to support findings. There are methods of meta-analysis where results of many studies are examined together so that the pooled probabilities can be calculated with some degree of accuracy, even though there may be some complications of interpretation because different studies will have widely different hypotheses.