Aparna,
The first service is failing when trying basic queries, support can help you work through this
http://ca.dep.state.fl.us/arcgis/rest/services/OpenData/AQUATIC_PRESERVES/MapServer/0/query?where=1=1&f=json
The second problem seems to be transient. I reset the download and it is working fine. Please note that the only the refresh button next to each dataset will reset the download. The button at the top of the list will not actually reset the download.
Although I was unable to reproduce your issues in our QA environment, we will continue looking for a permanent solution.
Daniel