You said next week, so is it AC563 on 23 DEC? If so, it is showing that R class does not exist on that flight (and interestingly, neither does Z class). You cannot wait list for a class that does not exist. I'm not sure if this is intentional by AC or it is an IT glitch. Also, given that the flight is showing as Y0, it is likely completely full or oversold in Y.
Results from ExpertFlyer.com
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Flight Availability Search
Departing SFO on 23/12/12 0:00 for YVR
Flying AC
Direct/Non-Stop Only
Exclude Codeshares
Frequency
Flight Stops Depart Arrive Aircraft Reliability Available Classes
0 Connections
AC 559 0 SFO YVR E90 Daily J4 C4 D3 Z2 Y8 B8 M5 U3 H3 Q0 V0 W0 S0 T0 L0 K0 N0 G0 P0 E0 A0 R1
23/12/12 7:00 23/12/12 9:18 75% / 10m
0 Connections
AC 563 0 SFO YVR E90 Su,M,T,W,Th,F J2 C2 D1 Y0 B0 M0 U0 H0 Q0 V0 W0 S0 T0 L0 K0 N0 G0 P0 E0 A0
23/12/12 11:40 23/12/12 13:58 38% / 55m
0 Connections
AC 565 0 SFO YVR E90 Daily J2 C2 D1 Z1 Y4 B4 M0 U0 H0 Q0 V0 W0 S0 T0 L0 K0 N0 G0 P0 E0 A0 R1
23/12/12 18:55 23/12/12 21:10 57% / 24m