Intersect fails for local point FC and hosted feature layer

[GabrielMarcus1]

I'm attempting to intersect some points with a layer hosted by ESRI: Flood Hazard Layer and can't
I've also tried to use the FEMA NFHL hosted on their site (both using the ArcGIS server and OGC WFS)

On the ESRI layer:

PW Intersect fails with ERROR 160203 which has a very unhelpful description which is essentially just the title.  
Intersect "succeeds", but has an empty output, which seems odd because I can see that the point is inside the polygon with no holes. If I select a containing polygon and perform the intersect, it works using either tool. 

Both the point and polygon layers are the same projection. The point layer exists on a local drive, the FC is hosted by ESRI. 

I've tried to export the "USA Flood Hazard Reduced Set" but not all of the data is exported, which also seems odd. Does anyone have another solution?

[JayantaPoddar]

The issue could be due to the timeout setting of the services.

How many points do you have? 

You could use a smaller subset of points for intersection. Or a smaller selection of flood hazard areas for export.

According to USA Flood Hazard Areas , you could

• Use as an input to geoprocessing. For example, copy features allows you to select then export portions of the data to a new feature class. Areas up to 1,000-2,000 features can be exported successfully.

[GabrielMarcus1]

Around 600 points across CONUS is what I have. 
I could use a smaller subset of points, but they're geographically distant so I would probably be better served going to FEMA MSC site and entering each address in, which I was hoping to avoid doing. 

I would like a local copy of this file, but I can't seem to get it. There are a few sites that have copies (ESRI, HIFLD, FEMA MSC) but when I go to download, or copy the GDB to my AGOL account, it always times out. Even filtering the data seems to be too large. 

You mentioned a limit of 2,000 features. Is that a default setting likely to be in common use?

[JayantaPoddar]

The limit is not on the number of features, but the timeout period. So your system configuration, network speed, etc. will also have an impact. Even the coordinate system of your point data impacts the performance.

Try projecting the point data to Web Mercator (Auxilliary Sphere) WGS 1984. Ensure the coordinate system of the map is also the same.

In case you have a high-end machine, could you also test Pairwise Intersect (Analysis) 

Could you share the point data or a sample  (100 points) of it? Just want to try it out before providing any further suggestion. I was able to intersect with 3000+ points