Per the 2.3.4 manual, if this helps:
Synchronizing your conversations by label
The Gmail webmail service has the resources to store all the messages you’ve ever
sent or received; your phone does not. To save space, Gmail downloads only some of
your messages to your phone. You can set which conversations’ messages are kept
current on your phone, by label, and what portion of those conversations, by time.
You use the Settings application to control how and when applications synchronize
their data. See “Accounts & sync settings” on page 373.
Select which labels to synchronize
1
Open your Inbox.
2
Press Menu and touch More > Settings > Labels.
The Synchronization settings screen opens, displaying a list of your Gmail labels,
for the account listed at the top of the screen. Below each label is its current
synchronization setting: Sync all, Sync 4 days, or no label (not synchronized).
3
Touch a conversation label whose synchronization settings you want to change.
A dialog for that conversation label opens, with three options:
Sync none
Don’t download any conversations that have only this label.
Sync 4 days
Download the previous 4 (or number of days you set) of
conversations.
Sync all
Download all conversations with this label.
Gmail 157
AUG-2.3.4-106 Android User’s Guide
Set how many days to synchronize
1
Open your Inbox.
2
Press Menu and touch More > Settings > Labels.
3
Touch Number of days to sync.
4 Enter the number of days and touch OK.
