For some people holding the Ukulele is the most difficult thing to learn.

Some ideas:

• consider buying a strap to help you until you become more comfortable with it
• roll up your sleeves so that flesh is touching the instrument as cloth can be slicker than your skin.
• think about holding the body of the ukulele with a little ‘pinch’ between your ‘elbow to upper arm’ and your rib area  (think slight pressure OR even more pressure if it is not working).  Should still be comfortable, just focused pressure.   You may find that the fretboard is further away from the body (forming a larger triangle of space between you and the ukulele).
• Concentrate on ‘holding the instrument’ before thinking about playing chords.

Here is a good introductory video about playing the Ukulele in less than 10 minutes.  Beginning about 1:51 he discusses holding the ukulele.

For a larger ukulele (tenor or baritone) you might try the suggestions in the following video:

Here is a good video about holding the left end of the ukulele: