Depends a lot on how native they go. If they become sufficiently intergrated onto the politcal and economic situation of the Levant they could last rather longer even without the manpower. Of course if the manpower thing were solved they would still become increasingle estraged from Latin Europe (recall the differences involved stances on forced conversion and killing every muslim in sight).
I should be more specific on what I mean by "manpower"- I mean European knights. The Latin Armies were based on heavy calvary (knights) and needed more land in order to support more knights. This is basically part of a larger need for greater strategic depth. The only way to increase European manpower was to expand into Syria (via either Aleppo or Damascus). This expansion would both increase manpower and create a large buffer for the Latin East. Basically, if Aleppo and Damascus can both be captured, then there the Latins would be able to significantly reduce the threat from the East. Basically, Syria forms a rather nice little unit, and if you can take that unit, then it there is not another base to launch an easy attack on any Syrian city.
A totally Latin-occupied Syria would be able to survive for a long time. It would have the manpower to be able to beat off Muslim invasions, and would control the end point of the Silk Road, so it would have a lot of economic might. Further military expeditions could be launched north, to aid the Byzantines in their war against the Iconium Sultanate, or south, into Fatimid Egypt.
The politics of such a Latin state would be really cool, because you have the Kingdom of Jerusalem, occupying some spiritually important land (and thus $$$ from pilgrams), while the Counts of Aleppo and Damascus would be fighting over market share from the Silk Road. The Latin lords who rule Aleppo and Damscus are going to very rich princes, who will probably be able to be basically independent of the Kingdom of Jerusalem (and the Byzantine Empire). If a King of Jerusalem gets Aleppo though, he may be able to use the economic leverage from that possession to unify the kingdom. Your also going to be dealing with some cool urban politics. I bet that with Latin control of the end point of the Silk Road, you'll see more conversions to Latin Catholicism among Arab merchants, who will probably face legal prohibitions on trade if they remain muslims. The trade wealth in Damascus and Aleppo could even lead to a situation like in Italy, where successful merchants are able to marginalize or overthrow their princes. Additionally, death was common among the Eastern Latins, and this would probably continue even with larger numbers of Latins. Things like legitimizing bastards will probably be common (I think it already was OTL) in order to keep family lines going. This is going to contribute to an interesting political situation, with bastards running counties, and Arab Merchant-Princes running cities.