Adding an array item with += drops custom AliasProperty

Code:
$a = @(1,2,3)
Get-Member -InputObject $a -MemberType AliasProperty "`nadd AliasProperty 'size'"
$a = Add-Member -InputObject $a -MemberType AliasProperty -Name 'size' -Value 'Length' -PassThru
Get-Member -InputObject $a -MemberType AliasProperty "`na.size=$($a.size) ($($a -join ','))""a.length=$($a.length)""a.count=$($a.count)" 
$a += 4"`nAdded item to array and AliasProperty 'size' is gone!"
Get-Member -InputObject $a -MemberType AliasProperty "`na.size=$($a.size) ($($a -join ','))" + ' *** notice the missing value for $a.size'"a.length=$($a.length)""a.count=$($a.count)" "`nadd AliasProperty to array again"
$a = Add-Member -InputObject $a -MemberType AliasProperty -Name 'size' -Value 'Length' -PassThru""
Get-Member -InputObject $a -MemberType AliasProperty "`na.size=$($a.size) ($($a -join ','))""a.length=$($a.length)""a.count=$($a.count)"
Output:
   TypeName: System.Object[]
Name  MemberType    Definition    
----  ----------    ----------    
Count AliasProperty Count = Length
add AliasProperty 'size'
Count AliasProperty Count = Length
size  AliasProperty size = Length 
a.size=3 (1,2,3)
a.length=3
a.count=3
Added item to array and AliasProperty 'size' is gone!
Count AliasProperty Count = Length
a.size= (1,2,3,4) *** notice the missing value for $a.size
a.length=4
a.count=4
add AliasProperty to array again
Count AliasProperty Count = Length
size  AliasProperty size = Length 
a.size=4 (1,2,3,4)
a.length=4
a.count=4
Is there another way to add an array item and preserve the custom AliasProperty?
Thanks,
Jim Cox