The skipping stitches may not have to do with how you basted the quilt. It could be that your machine has gone slightly out of time. Have you tried regular stitching to see how that works? If it is okay, the timing may be off just enough that some of the tension changes while FMQing no longer work. Stitches are formed by very accurate timing between the needle and bobbin mechanisms. FMQ puts varying tension on the thread, unlike regular stitching.
If you have a machine where you can reach the upper tension discs, you may want to clean between those (unwaxed dental floss works well, or use several strands of thread twisted together to "floss" the tension discs).
Also, check that the upper thread is feeding smoothly to the machine. If you are using a cone, a thread net may be necessary.
One last thing to try is a larger needle (one size up). If something about the way you are moving the quilt sandwich has changed, you may be causing the needle to bend slightly on occasion. This affects the stitch timing.
Last edited by Prism99; 10-02-2015 at 06:43 PM.