How can I rewire half switched receptacles?
Yes. The tab between the upper and lower sections of each of these outlets have been broken off on the hot (black) side of the receptacles. There are separate wires running to the upper and lower sections. One is always hot and one is switched.

On the outlet you want always hot on both sections, first determine whether the upper or lower section is the switched section. After the power is turned off, disconnect the black wire on the switched part of the outlet. Cap that wire with a wirenut (and tape for backup). Disconnect the black wire from the always hot side of the receptacle. Make two short pigtails of black wire (about 3-4" each), strip both ends of these wires and attach one end of one of these wires to the upper screw and one end of the other wire to the lower screw on the hot side of the receptacle. Twist the other end of these pigtails together, along with the always hot black wire coming into the box.

This is effectively re-establishing the connection that was removed when the tab between the upper an lower sections was removed to make one half switched.

If there is only one white wire going to the receptacle, you don't need to do anything to that wire.  However, if there is a separate white wire going to the switched half of the outlet, the tab on that side may also be broken, and then you would need to treat it the same as the black.  That is, disconnect the switched white, cap it, create pigtails for the white side and attach them as you did with the black side.

Thanks to DoxyLover for pointing out the possible multiple circuit issue.

Supplement

As pointed out by @Johnny in a comment, an even easier solution is to replace the existing receptacle with a new receptacle that has intact tabs connecting the upper and lower sections (receptacles are very cheap) . Again, you would cap the wires connected to the switched half on the old receptacle, but then you only need to connect the black and white wires from the unswitched side to their respective screws on the new receptacle. The intact tabs will deliver power to both sockets on the receptacle.