I have a scheduled job that tallies up the names of all running processes every night. I've had this set up for a very long time.
First time I saw unsecapp.exe was June 18, 2013 (that was on Win 7 x64). Most recent time I saw unsecapp.exe run was June 30, 2014 (I switched to Win 8.1 in October, 2013).
Before that I saw it only intermittently, about once a month or a bit less. For example, these are the dates since the start of 2014...
TaskList_2013_06_18_02_30_00.log: "unsecapp.exe", Process ID 3392
TaskList_2013_08_11_02_30_00.log: "unsecapp.exe", Process ID 8112
TaskList_2013_08_12_02_30_00.log: "unsecapp.exe", Process ID 8112
TaskList_2013_08_13_02_30_00.log: "unsecapp.exe", Process ID 8112
TaskList_2013_08_14_02_30_00.log: "unsecapp.exe", Process ID 8112
TaskList_2013_08_15_02_30_00.log: "unsecapp.exe", Process ID 8112
TaskList_2013_08_27_02_30_00.log: "unsecapp.exe", Process ID 30268
TaskList_2013_08_28_02_30_00.log: "unsecapp.exe", Process ID 30268
TaskList_2013_08_29_02_30_00.log: "unsecapp.exe", Process ID 30268
TaskList_2013_08_30_02_30_00.log: "unsecapp.exe", Process ID 30268
TaskList_2013_09_10_02_30_00.log: "unsecapp.exe", Process ID 6312
TaskList_2013_09_22_02_30_00.log: "unsecapp.exe", Process ID 9764
TaskList_2013_09_23_02_30_00.log: "unsecapp.exe", Process ID 9764
TaskList_2013_09_24_02_30_00.log: "unsecapp.exe", Process ID 9764
TaskList_2013_09_27_02_30_00.log: "unsecapp.exe", Process ID 4984
TaskList_2013_09_28_02_30_00.log: "unsecapp.exe", Process ID 4984
TaskList_2013_09_29_02_30_00.log: "unsecapp.exe", Process ID 4984
TaskList_2013_09_30_02_30_00.log: "unsecapp.exe", Process ID 4984
TaskList_2013_10_31_02_30_01.log: "unsecapp.exe", Process ID 4236
TaskList_2013_11_01_02_30_00.log: "unsecapp.exe", Process ID 4236
TaskList_2013_12_13_03_00_02.log: "unsecapp.exe", Process ID 11888
TaskList_2014_02_08_03_00_59.log: "unsecapp.exe", Process ID 5452
TaskList_2014_02_27_03_00_02.log: "unsecapp.exe", Process ID 17520
TaskList_2014_04_25_04_00_02.log: "unsecapp.exe", Process ID 8072
TaskList_2014_05_07_04_00_01.log: "unsecapp.exe", Process ID 1688
TaskList_2014_06_30_04_00_02.log: "unsecapp.exe", Process ID 8600
Based on the above evidence, I'd say it's started only occasionally, and may be persistent (noting multiple entries for subsequent days with the same process ID). I don't boot up very often.
Edit: I have NEVER run the Avast Browser Cleanup Tool.
-Noel