Texas would have to overcome the following factors in favor of annexation:
1) Texas lacked resources to both protect itself and secure its sprawling land claims (NOT just the Nueces-Rio Grande region BUT also claims on further Mexican territory e.g. the expedition to Santa Fe 1842);
2) Texas' economic development was spurred by mass Anglo-American immigration which further skewed politics towards dependency w/America (and more particularly, the South + cotton economy);
3) Texas' position along the all-weather Southern route to California made it a key strategic location for US expansion to the Pacific under Manifest Destiny;
4) European nations were unwilling to recognize or loan money to Texas, mainly because their banks had significant loans with Mexico.
On the other hand, there were also factors encouraging Texan independence:
a) Mexico would fight the US over Texian annexation;
b) US Whigs were generally opposed to US expansion and especially to expansion of slavery, which was legal in Texas;
c) The possibility of losing land claims to other US states after annexation, important since a lot of Texian settlement/economic activity came from Texas' policy of free ownership of land and land speculation.
Historically, the (vastly overblown) fear of a Mexican-Native American alliance to crush Texas drove Texian foreign policy. Houston attempted to reconcile with both by reserving land for NAs and by border stabilization with Mexico; his successor Lamar wrecked these policies through aggression and removal (both of Tejanos and NAs). After that, Texas really had no more options for its own security other than siding with the US. Ironically, Lamar was far less in favor of annexation by the US than Houston was.
As long as the Whigs or some similar anti-slavery party are in power in the US (and their electoral base remains mainly in the industrial North), annexation is unlikely. At the same time, a more aggressive US Caribbean/Mexican policy (which would likely morph into Confederate policy given a successful civil war) driven by Southern Democrats may also reduce the likelihood of annexation as Europeans use Texas a buffer/irritant against further US designs.
The best case for independent Texas is as follows: accommodationist policies with Mexico cause the latter to drop its fierce opposition to Texian independence, winning the Republic critical European support (and loans to support its bankrupt government). In the meantime, US Whigs snuff out any possibility of Texian annexation. The result is that Texas can economically develop with the help of Anglo-Americans BUT without being incorporated into the US. Once the first few decades are over, an independent Texas would be the status quo position as far as everybody was concerned.