With most palms if you pull on the spear and it comes out it is dead. But for some reason when I did this to my dead mexican fan palm, it didnt pull out until a few weeks later. Just give the center leaf coming out a good tug. If it flies out or even moves around a little, its dead. Also if that center leaf is brown, survival is really lessened greatly. If the center spear is still green than it has a chance for recovery and with some waiting and some heat, it should recover.

Good luck!

I'm not saying it's a good sign to suffer center spear loss, but I have even had Washingtonias recover from bud loss. Though the plant will be delayed a year and vulnerable to next winter.

I'm in the Austin area and all the Mexican Fans, including mine took a beating this winter. That said, mine's still sad looking but has been pushing our new fronds for the past few weeks.

I wouldn't give up just yet!