No, if you lost money you will still recharacterize the full contribution amount but you will transfer less to the traditional IRA. The losses are deemed to have taken place in the traditional IRA because with a recharacterization you pretend that you never made a Roth contribution but made a traditional IRA contribution.
For example, if you made a $5,000 contribution to the Roth IRA and had a $500 loss and recharacterized it you will enter $5,000 as recharacterized but only $4,400 get transferred. If you make the contribution nondeductible then you would show a $5,000 basis on Form 8606 (the contribution amount).
@DiverJudge
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