There is both an overall storage limit (~ 40 MB) per experiment as well as a cap in the upload components (~ 20 MB at once, if I am not mistaken) as a security measure / to prevent certain types of attacks on the server. Depending on the number of files you are aiming to upload and their respective sizes, it may well be that you are hitting one or both of those limits. Uploading the files in smaller chunks would be the way to deal with the uploader cap. If the total storage amount required exceeds the 40 MB limit, hosting those files on your own web space would be a viable option.
Hope this helps.