There's no hard an fast cut-off today. A few years back it was around 100 links. I'd say if the target urls for your 1,000 links aren't even getting indexed, then you do have too many links on that page, and you also need some other click path navigation to those deep pages.
Also realize that backlinks may play into the picture when you're trying to get more of a site indexed. Plus, this is not a good time to depend on the site: operator for the number of indexed pages. It seems to be unusually inaccurate right now.