There's no easy answer here because each Federal government system is different. Let's contrast the EU with the United States (both are Federal systems in a general sense)
How strongly united the people are
More concisely, how nationalistic are the people for the Federal system? The United States has a pretty decent cohesion overall. Few people were cheering when the September 11 attacks happened. By contrast, the European Union is trying to unify multiple separate countries, each with its own people, economy, and, in many cases, language.
The first official languages of each of the 28 Member Countries has the status of an official language of the European Union. In total there are 24, with Irish, Bulgarian and Romanian gaining official language status on 1 January 2007, when the last two countries joined the European Union, and Croatian becoming official in 2013.
It's also worth noting that some countries in the EU (notably Germany) hold more power (respectively), thanks to their GDP and population size.
How strong the Federal government is
The EU doesn't have absolute power over its members, unlike the US where Federal laws trump state laws. Wikipedia describes EU state sovereignty like this
While the member states are sovereign, the union partially follows a supranational system that is comparable to federalism. Previously limited to European Community matters, the practice, known as the "community method", is currently used in most areas of policy. Combined sovereignty is delegated by each member to the institutions in return for representation within those institutions. This practice is often referred to as "pooling of sovereignty". Those institutions are then empowered to make laws and execute them at a European level.
Because each state is its own country, secession is a very real threat to the EU (see brexit for a prime example).
Most US states, however, lack their own country-level mechanisms (Federal Reserve, military, diplomatic channels, etc). These present a serious barrier to secession. Additionally, the US Constitution has no provisions for secession, unlike the EU, and numerous legal rulings against it would make it very difficult (not counting the US civil war, which was fought over the issue).
How tightly integrated the economies are
The US shares a single economy. The EU mostly shares an economy, but some members (i.e. the UK) opted to keep their own currency. But the real problem the EU has faced is that some countries abused the economic union
The 2001 introduction of the euro reduced trade costs among Eurozone countries, increasing overall trade volume. Labour costs increased more (from a lower base) in peripheral countries such as Greece relative to core countries such as Germany, eroding Greece's competitive edge. As a result, Greece's current account (trade) deficit rose significantly.
As the Great Recession spread to Europe, the amount funds lent from the European core countries (e.g. Germany) to the peripheral countries such as Greece began to decline. Reports in 2009 of Greek fiscal mismanagement and deception increased borrowing costs; the combination meant Greece could no longer borrow to finance its trade and budget deficits at an affordable cost.
A country facing a “sudden stop” in private investment and a high (local currency) debt load typically allows its currency to depreciate to encourage investment and to pay back the debt in cheaper currency. This was not possible while Greece remained on the Euro. Instead, to become more competitive, Greek wages fell nearly 20% from mid-2010 to 2014, a form of deflation. This significantly reduced income and GDP, resulting in a severe recession, decline in tax receipts and a significant rise in the debt-to-GDP ratio. Unemployment reached nearly 25%, from below 10% in 2003. Significant government spending cuts helped the Greek government return to a primary budget surplus by 2014 (collecting more revenue than it paid out, excluding interest)
This crisis lead to a lack of confidence in the Euro, and the economic union as a whole (with some calling for Greece to be expelled from the Euro) and likely helped play a role in Brexit