If you use an Energy Search and don't find any Basic Energy, do you still discard the Energy Search?
Yes, you would still discard it.
Source: PUI Rules Team (2004-01-15)

Relevant cards

Note: All applicable cards may not be listed below.
BW1_93
BW7_128
DP1_117
DP5_90
EX1_90
EX10_94
EX14_86
SWSH1_161
SWSH1_161
TK1-Latias_9
TK1-Latios_9
TK2-Minun_9
TK2-Plusle_8
TK3-Lucario_8
WOTCE1_153
WOTCFO_59