What makes you think they had less natural resources than Europeans? In reality they were better off than Europeans, because thy could trade with China, India and Europe directly, not to mention that the crusader kingdoms were surrounded by Muslim areas on most sides and that put them in a disadvantage.

I should probably start out by clarifying a few things. Firstly, throwing around the word 'empire' is a risky business when we discuss history. What does and doesn't constitute an 'empire' is a messy business but almost no definition of it can be applied to high medieval Muslims in the Middle East pre-Saladin and I'd be wary of doing it even after him. Even more problematic, though, is the idea of 'winning' the 'Crusades.' Winning in Medieval warfare can be a weirdly unclear thing, there's not a lot of abject surrender nor total annihilation (despite what you might expect). Battles obviously have a clear winner and a loser but overall wars are a bit harder to determine. Warfare is such a constant in the Middle Ages that it's hard to say exactly what is and isn't part of a war and who is and isn't winning. For example, when talking about the Hundred Years War you have the major conflict between England and France but you also have the side conflicts of The Black Prince's campaigns in northern Spain and the Breton War of Succession. These sort of involve major players in the HYW but not in the main conflict and it's not really clear exactly if they should all be seen as one big conflict or separately and now that we can't even define the limits of the major war how can we say who exactly is winning? It's messy is what I'm saying really.

The biggest issue, though, is that the Crusades has two meanings. It can mean the primary period of warfare in the Holy Land between Christians and Muslims starting in 1096 and ending a while later (when it ends depends on your definition really) or it can mean just the specific campaigns preached by the Papacy. When we number the Crusades we are taking the latter meaning but the Crusaders didn't entirely limit themselves to these moments to wage war in the Holy Land and the Muslims living their certainly wouldn't be defined in that way.

To answer your question, however, the Crusades weren't exactly a war between all Christians and all Muslims. Trade between Europe and the Middle East didn't stop during the Crusades, in fact it likely increased quite a bit. Since the Crusader States (those territories controlled by Western Europeans) included several large ports (like Jaffa near Jerusalem) they were actively engaged in trade. The thing is that the far east is still a long way from Syria so most of the trade would have had to pass through Muslim merchants along the way. This wasn't even seen as a problem, the Crusaders living in the Middle East were hardly going to refuse to deal with Muslims. Muslims were the vast majority of people in the region. This is to say nothing of the inevitable trade connections with Byzantium.

The Western European's failures in the later Crusades is hardly a result of funds alone as well. Chaos in the Crusader States as well as a near constant lack of soldiers caused huge problems for them and the actual major Crusades launched were often a tactical and logistical mess (especially the Second). Muslim leaders were also hardly broke. Egypt was still a major trade center as was Damascus in Syria.

If you want to read more on the Crusades I strongly recommend Thomas Asbridge's The Crusades. It's a very easy to read book and he covers a very wide range of topics related to the Crusades. Amin Maalouf's The Crusades Through Arab Eyes is also a great introductory work if you're curious about the Muslim perspective on the Crusades.