FWIW, your app is likely to be much more reliable if you stop relying on the Finder for this sort of thing. It's AppleScriptObjC -- use the ObjC part:
set anNSURL to (current application's |NSURL|'s fileURLWithPath:"/Volumes")'s URLByAppendingPathComponent:serverName
set theResult to (anNSURL's checkResourceIsReachableAndReturnError:(missing value)) as boolean
if not theResult then
-- not mounted, so handle error
end if
set {theResult, theSpare} to anNSURL's getResourceValue:(reference) forKey:(current application's NSURLVolumeAvailableCapacityKey) |error|:(missing value)
if theResult as boolean then
set spareString to (current application's NSByteCountFormatter's stringFromByteCount:theSpare countStyle:(current application's NSByteCountFormatterCountStyleFile)) as text
else
-- couldn't get the value, so handle error
end if