Assuming you have selected the quilt before trying to select "solidify", you can easily troubleshoot your model to look for those small edges that are causing the headache. Build a flat surface that intersects the entire model using an offset datum plane as your sketching plane. Merge this surface into the model and keep the volume inside of the new flat surface and above or below the falt surface. Try solidifying the resulting quilt volume. If it solidifies you are in good shape. You can then adjust the value for the offset datum plane used for the flat surface until the solidify feature fails. The spot where it fails is where your gaps are located. If it is a large/complex model you can add a second flat surface perpendicular to the first and manipulate that in the same way.
If you have BMX you can do as I suggest above and have the software manipulate the offset datum for you, You can track the mass or volume of the part. The resulting graph for the volume will show where that calculation goes to zero. That is your problem spot.
Or you can old school it if you have good eyes. Set the working window background color to the same color as stitched edges in your quilt. You might be able to then see the edges that are a color other than the background color. This worked a bit better when seams were magenta and open edges were yellow.
I hope this makes sense...and helps.