Paragraph abuse
A text normally consists of numbered chapters and sections. LaTeX provides two hierarchical constructs to make a further subdivision without numbering: the paragraph and the subparagraph.
These are conceived as run-in headings, i.e. the text after them continues on the same line. You can see them in their normal form below:

\paragraph{Lorem ipsum} Lorem ipsum dolor sit amet, consectetuer
adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa. Cum
sociis natoque penatibus et magnis dis parturient montes, nascetur
ridiculus mus. Donec quam felis, ultricies nec, pellentesque eu,
pretium quis, sem. Nulla consequat massa quis enim. Donec pede justo,
fringilla vel, aliquet nec, vulputate eget, arcu.
Sometimes, it makes sense to put a newline after the paragraph run-in heading. Like so:

\paragraph{Lorem ipsum}~\\
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean
commodo ligula eget dolor. Aenean massa. Cum sociis natoque penatibus
et magnis dis parturient montes, nascetur ridiculus mus. Donec quam
felis, ultricies nec, pellentesque eu, pretium quis, sem. Nulla
consequat massa quis enim. Donec pede justo, fringilla vel, aliquet
nec, vulputate eget, arcu.
The trouble is that the newline is considered to be a breakable space. Therefore, you might find yourself in a situation where LaTeX put the run-in head on the bottom of a page to let the text start on the next page. This is what is called an 'orphan' in typesetting lingo. With ordinary section headers this will never happen. However, LaTeX does not consider the paragraph heading to be any more special than ordinary text.
There are two solutions:
- one good for the occasional use: introduce an unbreakable newline
- one good if all your paragraphs need a newline: redeclare the paragraph to be a sectioning command
Occasional

\paragraph{Lorem ipsum}\mbox{}\\*
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean
commodo ligula eget dolor. Aenean massa. Cum sociis natoque penatibus
et magnis dis parturient montes, nascetur ridiculus mus. Donec quam
felis, ultricies nec, pellentesque eu, pretium quis, sem. Nulla
consequat massa quis enim. Donec pede justo, fringilla vel, aliquet
nec, vulputate eget, arcu.
Systematic
Put the following in your preamble:
\makeatletter
\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}%
{3.25ex \@plus 1ex \@minus .2ex}% space before
{.5ex \@plus .2ex}% space after (positive => block, not run-in)
{\normalfont\normalsize\bfseries}}
\makeatother
I guess you are smart enough to do something similar with subparagraphs as well.