Hi lo13579,
I suspect that your Illustrator files are very complex ones with transparency and special effects.
What's your operating system version? How many memory is installed in your machine? 16 GB is recommended. Is there enough room on your hard disk so that some GBs of free space are there?
FWIW: Obviously your workaround saving your AI files to EPS is OK with you.
However: With EPS some features are not possible: Live transparency and color management. And that can lead to unpleasant surprises when you deliver pages as exported PDF files from InDesign to the printing company.
The alternative to EPS:
Save your AI files to PDF/X-4 with no image downsampling and place the PDF on your InDesign pages.
That would be the best solution, I think.
Keep one copy of your artwork as AI file, as a working file so to say; use the PDF for your production with InDesign.
If that is not working, please come back and we find a way to troubleshoot all this using Acrobat Pro's vast sets of preflight functionality and methods of diagnosis.
Regards,
Uwe Laubender
( ACP )