Word/Idiom/Phrase to describe a stage in a project's life-cycle when you are stuck and thus no progress is happening?

Solution 1:

You could say, the project stalled/stalled out (or came to a stall or is in a stall)

stall: to come to a standstill AHD

Solution 2:

If you need to emphasize there's an issue blocking further progress, you could say "the project is blocked":

The resources indicator will display at a glance whether a project is blocked in terms of resource allocation.

(www.nqicorp.com)

UPDATE: You could also say the project is stagnant, which implies there's lack of activity or progress:

stagnation: a situation in which there is no progress or development

(Macmillan Dictionary)

In the context of, say, a software project, stagnation might happen for reasons such as:

1. lack of interest on the part of the developers
2. the vagueness of the business case
3. the project is sidelined due to other other projects taking priority

To fix stagnation issues you need to invigorate the project and breath new life into it.

Solution 3:

Impasse fits this perfectly. MW-Link.

a situation in which no progress seems possible

In American usage, this word is often used to describe negotiations. Once the negotiation process reveals an issue on which both sides are unwilling to compromise, an impasse has been reached. In the legal context, an impasse may be formally declared, indicating that the current round of negotiations has reached a stalemate.

In both cases, the existence of a problem is assumed.

Solution 4:

We often use the term roadblocked in tech.

roadblock noun

something that blocks progress or prevents accomplishment of an objective MW