Exporting a project takes a very long time and might even crash when performing an export.
One of the reasons that might cause this is the large size of the project (a lot of training batches and/or work batches).
A way to work around this might be to export the project without the training batches first and then update it to synchronize the training batches separately. This should limit the resources that are required for the export operation and would allow to split it into 2 operations.
An additional option to consider is downloading the project first, then syncing the training batches without the samples (just the trained layouts), and then syncing the training batches again with the respective sample images.
There is also a possibility to only download specific batches with specific IDs - it is possible to download or sync the project with a local copy in smaller portions, only specifying specific batch IDs in the process.
All of these options are specified in the aforementioned FCAdminTools documentation:
Centralized Project Administration