If you want to get the results as you see them on the screen without anything shortened, you might try changing your code like this:
$events = Get-WinEvent -ea SilentlyContinue `
-ProviderName "Hyperion Financial Data Quality Management - Task Manager Service"|
Where-Object { $_.TimeCreated -gt [datetime]::now.AddMinutes(-15) -and $_.Message -match $pattern }
$events |format-table -AutoSize |out-file -append -encoding Ascii G:\Sysadmin\FDMmonitor\Error.txt -width 300