Yes, there is a limit.
We're aware that our Term Enrichment tool on the homepage of the Gene Ontology Website cannot handle very large gene lists. The root of the problem is that at a certain number, the input (gene list) is too large for the form; however there is not an exact number at which it fails. One way to solve the problem, should you come across this situation, is to reduce the size of the input file by reducing the number of genes.
Alternatively, annotators can use the PANTHER Term Enrichment tool directly, without AmiGO as an intermediary; this would still be the exact same analysis with the GO data. To perform term enrichment analysis directly from the PANTHER website, visit http://pantherdb.org. Once you upload or paste your gene list, select the 'Statistical overrepresentation test' option (in Step3) to perform the term enrichment.
Although we would like to correct this as quickly as possible, we may not be able to immediately address the matter. You can keep track of our progress on this particular issue following this entry in our bug tracker on GitHub: https://github.com/geneontology/amigo/issues/198
We will try to have a fix prepared and put into production as soon as possible.